Thursday, September 1, 2016

BBA II Semester English Notes



CHAPTER TWENTY
HOW SANE ARE WE?

LITERAL COMPREHENSION

The concept of wise and good rulers is merely imaginary. In fact, our collective decision making process is unreasonable. Let us take the example of the use of CFCs (chlorofluorocarbon). Some 20% of green house effects is caroused by CFCs. Also, they will reduce the ozone very much. If this very thin protective shield (sjr) is destroyed. The ultraviolet radiation of the sun will disturb natural eco-system, lower agricultural productivity, suppress the human immunity system and raise the incidence of skin cancer and eye cataracts.

INTERPRETATION

CFCs are use as coolants, foam-blowing against, propellants and cleaning against in computer chips. If these long live substances reach the stratosphere, they will reduce the ozone layer. No one has so far paid any serious attention to the scientist's warning. The government and CFC makers have delayed to ban their use. And their harmful effects have already been seen in Australia and Chile.

CRITICLA THINKING

Some considered that the decision of phase out their global use is a proof of collective misbehavior. In 1974 scientist warned about their harmful effects, but there was a long gap between the warning and their ban. So these people compare the ozone tale to Karel Capek's "war with Newts". In this science fiction, highly productive salamanders were protected from sharks, their controllers by their discovers in exchange for pearls. These creatures were use for the other purpose too. Soon they ran out of living space to accommodate their growing numbers. They flooded countries, one at a time. At the end, humanity was in danger not by the Newts but by the greed. Short- sightedness and great stupidity of human beings.

ASSIMILATION

The world is not a completely rational place. In 1935 there was only one enemy, Hitler but now there are many more enemies. Like the Newts. We are reproducing at a surprising rate. Our weapons have becomes for more destructive. If we don’t think and do politics sensibly, we may put humanity in danger.







CHAPTER TWENTYONE
TO KNOW FLY

LITERAL COMPREHENSION

Scientific experiment beginning with an act faith and continuous with an observation and a question. It is scientist's way of asking nature of question. They changes condition observe a result and draw a conclusion. But these most be purpose experiment control and co-relation with cause and effect should not confused.

INTERPRETATION

By asking write question and by observing cleverly a scientist can find out what the fly's sense of test is. Flies walk about in the food and constantly bring out their proboscis when they see on sweet things, they louder their proboscis (tongue). The biology's first guess that tasted with its feet.



CHAPTER TWENTYTWO
KING JOHN AND THE ABBOT OF CANTENBURY

LITERAL COMPREHENSION

King John was jealous of Abbot of Canterbury for his house keeping and good name. The Abbot was sent for and the king asked him three questions. He also told him that if he could not answer the questions, his head would be removed from his body. The questions were :( 1) what was the price of the king with his crown on his head? (2) How quickly could the king ride around the earth? (3) What was the king thinking at the moment? The Abbot could not answer them immediate and asked for two weeks time. Then he went to Cambridge and Oxford University to get the help of the scholars there. When nobody helped him, he came home looking very sad. But his shepherd (e]8fuf]7fnf) promised to help him. Them getting dress like the bishop, he went to king john and answer all his questions. First, he replied that the king's price was twenty-nine pence because Christ was sold for thirty pence and that he was one penny worse than the Lord. Secondly he answered that if the king rode at the speed of the sun when it rose in the morning he could go around the earth in 24 hours. Thirdly he said that the king was thinking that the Abbot of cantenbary was answering his questions. But it was his shepherd that was answering. The king was satisfy with all the answers and pardoned the Abbot and gave the shepherd four nobles a week

INTERPRETATION

This poem might be trying to tell us that a common man can be wiser than educated person. It may also be interpreted to mean that everyday reality teaches man more than a library of books can.



CRITICAL THINKING

When I read this poem I was quite surprised to know that so difficult questions can have so simple answers. We are very please with the witty (a'lbdQfk"0f{) answers of the shepherd.

ASSIMILATION

This poem had thought me the value of the common people. Previously I used to think that being an under graduate student I was for more superior to my illiterate neighbors. But now my false pride has been shattered (6'sf6's).
I have started to respect them and expect practical advice from them.


CHAPTER TWENTY THREE
THIRD THOUGHT

LITERAL COMPREHENSIN

The narrator's friend was not a successful businessman. He always bought of thing at a high price and sold at a low price. But one day he bought a genume turner for 10 shillings and sold for 50 pound considering the good nature of dealer. He wanted to share the half of the profit with him but when he reconsidered, he did not like to be an idealist. He supposed that 10 pound would be in off. He again thought that if he gave him 10 pound the sellers would always expected money from every and spoil him business. So he decided to give him 5 pound. He then found a new option. If he gave him 5 pound the goodness of business would be angry. So 1 pounds gift would be enough. Afterwards he went to the club and loss all he had while playing cards. Then he came the conclusion that after the business had taken place there would be no obligation between the lealer and the customers.

INTERPRETATION

This essay might be trying to tell us that everyone become and idealist in the beginning and that the more he thinks the worse practical becomes. It may also be interpreted to mean that everyone is bad by nature and then he makes so many excuses to proved that he is not so.

CRITICAL THINKING

This essay has beautifully excused human nature . we try to find out excuses for everything we do, but don’t agree with the narrator's friend when he wants to share half of his profit. Is any one so much of a fool to share the profit? Does any one show his weakness to give the thing which he is not obliged to give?

ASSIMILATION

After reading this essay I come to understand myself batter. Like the speaker's friend I kept on barging with my soul. When I start preparation just the examination every year I promised that I will do it early years next time but after the examination is over I find so many excuses for not doing so and sometime I cant take an examination too. Changing opinion and making them suitable to what one likes is human weakness.











CHAPTER TWEENTYFOUR
WHO WAS TO BLAME

LETERAL COMPREHENSION


INTERPRETATION
Pyoter Demyanitch, the narrator's uncle and high school teacher decided to train a kitten when his hat and book were eaten by mice. When the mouse was trapped in the mouse trap, the kitten was brought closer to the trap. The kitten sniffed (;'Wof]) it and looked around wonderingly. When the kitten and the mouse were released, the mouse ran under the sofa and the kitten under the table. The uncle dragged the kitten and shook him the air. Being frightened, he passed the whole night under stove. When another mouse was cut the next day, the kitten trembled and mewed piteously seeing the mouse and the trap. He jumped hide under the sofa when the mouse was released. The kitten was bitten. After the forth attempt the uncle decided not to train him. A year later, he grew in to a tomcat but when he saw a mouse he ran away although he was going to the she –cat to express his love. Like the cat the narrator also runs away when he sees his uncle with a Latin book

CRITICAL THINKING
When I read this story I came to know that we should learn things without being forced. Many of the parents want their children to read all the time. They do not allow to children to play. So the children are frightened of books and never become good students. Even now like the narrator I shiver (sfDg') when I see my father coming to me with book in his hand.
This story clearly brings out the theory of learning. If we read this story literally, we can not accept many of the things. How can the narrator imagine what is going on in the mind of the cat? Is it true that tomcat runs away seeing a mouse?


ASSIMILATION
This story might be trying to tell us that one should learn things naturally. The more one to force to learn, the more one dislikes and each frightened of it. It may also be interpreted to mean that punishment will have a negative influence on the learner.



CHAPTER TWEENTY FIVE
THE BURDEN OF SKEPTICISM
(SKEPTICISM=REFUSE TO ACCEPT A CALIM WITHOUT ANY PROOF)

LETERAL COMPREHENSION

Skepticism is found in every day life. If we have to buy a used car we examining it even if we do not have any ideas about the car. If we buy it without examining, we know that we may have to be sorry for it. In some cases we use skepticism, but in politics and commercials we do not use it. So we cheated a little. But if we do not use it in the case of medicine we have we have to bear a great loss.

INTERPRETATION

If we study the whole history of mankind, we find that they have always accepted some kind of popular belief system. The reason for this is that all human needs are never fulfilled. These unfulfilled needs may be satisfied by these beliefs. It is natural for us to have a desire to take our dead relatives. And we would be happy when we learn that our spirit does not die and our existence will not come to an end forever.




CRITICAL THINKING

There are many channels who claim that they can contact with the spirit of a person long- long ago. But these spirits do not answer any specific questions and they answer only general and vague (unclear) questions. Their specific answer would have helps us a lot to know about the society of the past.

ASSIMILATION

Skepticism is dangerous. So it is not taught in school. Skepticism and openness to new ideas are equally necessary for human progress. If we are too open, we will not be in opposition to tell a difference between what is good and what is bad. But, on the other hand, if we are too skeptical, no new ideas will find any place. Scientist forms new ideas in to their minds in the form of hypothesis and examining them closely. If their ideas are proved correct they will be accepted. If they are proved false later on, the scientists will accept that they have made a mistake. But religious and political leaders never accept what is against their principles, however wrong their ideas may be.














CHAPTER TWEENTY SIX
MR. KNOW ALL

LETERAL COMPREHENSION

The narrator was a white man and he did not like his cabin met, Max Kelada just because he was of an Egyptian origin. Kelada was sociable and within three days he new everyone in board. He would organize all games and lotteries. But he was a bit insistent (lh88L). He did not no that he was unwanted and the title "Mr. know all" given to him was a praiseworthy term he supposed. Once he claimed that he was expert in pearls and the pearls worsened by Mrs. Ramsay wear real once, not cultural once. Mr. Ramsay bed a hundred dollar on it. Then Keleda examining them closely and found that they were real. But as he was about to speak, he saw Mr.Ramsay's face turning pale. So he said that the pearls were not real. Although he was ready to become full for this, he said the happy conjugal life of the Ramsay. He gave a hundred dollar note to Mr. Ramsay but Mr. Ramsay returned it secretly to Kelada. Then the narrator did not dislike him entirely.

INTERPRETATION

This story might be trying to tell us that a man becomes great not by his color, but by his thoughtful action. Max Kelada is a great man because he considered the value of others people's life greater than his won personal respect. It may also be interpreted to mean that the whites are intolerant of the non whites. Even at the end of the story the narrator still heisted to praise Kelada.

CRITICAL THINKING

This story represents biased (one-sided) attitudes towards non-whites. The narrator hates Kelada because he was not white, so do all other passengers. Just on this ground, in spite of being hated by everyone, why6 was kelada ready to help them? Was he ignorant of their hatred as the narrator supposed? Was he not a noble person who considered the goodness of everyone?

ASSIMILATION

After reading this story I came to know a lot about the westerners. They do hate Asians and Africans. They are really narrow- minded. Although the writer's view may be different, he has clearly expressed the attitude of the whites.






CHAPTER TWEENTY SEVEN
KEEPING ERROR AT BAY

LETERAL COMPREHENSION

We can avoid silly errors if we follow a few simple rules. First, if the case can be decided by observation we should observe our selves. Without knowing the things if we supposed that we know it we make serious mistakes. The classical writers have made such mistakes.

Secondly, if we can not observe the matter we have to make ourselves aware of our own bias ( one sided) when we do not get the right region to support our conviction, we get anger. In knowledge, there is no anger. By comparing our opinion with that of these, we can be free from some kind of dogmatism (s6/kG7L). We have to read the purpose of the opposite party. We have to go abroad to broaden our minds. But we should not imitate the forgner foolish custom.
It we can not travel, we can have an imaginary talk with the persons who support opposite views.

Moreover we should not flatter our self-esteem. Both man and women claim that their own sex is superior and they can present strong argument to support their views. Similarly, every country man things that his own country is superior to all, in fact every one or every nation has his or its merits and demerits. If we are bias se highlight the merits and ignore the demerits. Thus we can prove our sex or nation is superior. If we are proud of being human beings we should look our self in the perspective of the universe. In the vast universe, human life is the brief event and their might be other superior creatures who suppose that human beings are insignificant.

Finally we should avoid fear. It is the main source of superstition and cruelty. If we can get rid of it, we start getting wisdom and we shall find out to the truth.




















CHAPTER TWEENTY NINE
THE TINNY CLOSET
Closet = small room
Mr. New bold = Roomer-tenant
Mr. Crosby = land lady

LETERAL COMPREHENSION

Mr. Newbold, a roomer in a mid western city in the USA, calls his land lady Mrs. Crosby. He asked her not to let anyone open his room because as long as he lives there it is his own room. Mrs. Crosby consoles him and he goes out. Then she calls-up her friend and both of them enter his room out of curiosity. Mr.Newbold also came in, but hides himself when the ladies came down stairs. Earlier the land lady supposed that he might be a spy (hf;';) or a criminal or a lunatic (kfun) or a communist. But now she has seen many beautiful hats in his room. She holding a women's large and graceful hat in her hand, then she find her hat- making roomer quite unusual. His cleanness has also surprised her. After this event she can not tolerate him and plane to send him out of her house. Mr. Newbold weeps at his helplessness, when the lady goes in to her kitchen later he recovers and takes a great hatpin in his hand and calls her with the intention of killing her.

INTERPRETATION

This play might be trying to tell us that we should try to live a normal life. Mr. Newbold, being a man, was unusually neat and clean and he would not allow any one to go into his room. So the landlady was suspicious (z+sfn') of him and went into his room secretly with her friend. As result she was victimized. It may also be interpreted to mean that jealousy and over curiosity are harmful.

CRITICAL THINKING

This play has beautifully presented how curiosity leads to destruction. But are all the land ladies are as curious as Mrs.crosby and break into the tenant's room? Are men as coward as Mr. Newbold? Do they weep when they are helpless? Can such a coward produce any harmful things to the landlady?

ASSIMILATION

When I read this play I came to know many things about human nature. It is human weakness to have a desire to eat the forbidden apple. When the secrecy is disclosed, it makes people more terrible. Human beings are never satisfied with their present situation. The more they know, the more they are upset.



Chapter thirty
TO HIS COY MISTRESS
Coy = shy
Mistress = beloved
LETERAL COMPREHENSION

In the first stanza, the speaker imagines a world in which lovers have unlimited time. In this situation her unwillingness to make love would be no crime. In a series of complement, he prays her beauty by saying that each part of her deserves to be praised for many years. The second stanza denies the first/ no one has unlimited time. The time allow to us is short and we are chased by "times winged chariot" and before as lies death with its emptiness. The speaker sees his mistress in her grave with the warms attracting that long preserved virginity that she had refused him. The conclusion maintains the sense of urgency. It argues for life over death. The lovers are like amorous bird of pray that devour their time using it up more quickly by living life to the full. We can not stop time but we can live every moment of life lively and vigorously (strongly)

INTERPRETATION

This poem expresses the speaker's desire for sexual union with the loved one and the abstract to that union. It usage a carpe demonetize the day argument in urging sexual union. The speaker means to say that life is short and uncertain, so one must enjoy all the pleasures one can.

CRITICAL THINKING

The three stanza in the poem have a logical relation to each other. The argument of the speaker may be summarized thus: if we had time enough your coyness would be no crime; but as he do not have unlimited time, your coyness is unacceptable; therefore you must give up your coyness and satisfy your desire.

ASSIMILATION

After reading this poem I am more convinced about the value of time. In fact "time and tide wait for no one." The wise size it and make their lives successful. Whether we pursue our study or we make love, time is equally important.

Chapter thirty one
THE TELEGRAM ON THE TABLE

LITERAL COMPREHENSION

Krishna looked at the telegram on the table. It had been laying there for weeks. It was about a tragic event and one of the friends from his village had expressed his sympathy. But Krishna was not touch at all. He did his everything works normally. He would explain Nepali arts and culture to the tourists in his own way. He had a great desire to go abroad with some tourist girl. He had nourished this dream and had not thought about his village. He was lost in the city life. But tonight the telegram on the table attracts him. He could not fall a sleep. He did not want to think about the telegram but he could not neglect it either. It haunted him and finally he wept bitterly thinking of his wife, who had died weeks before.



INTERPRETATION

This story might be trying to tell us that, the fate of many young people who came to the city and forget their home. They don't like to think of their pass lives. They live by dreaming of the batter future. It also informs us about their unhappy life.

CRITICAL THINKING

I agree with the writer when he describes the story of rural people visiting towns and cities. They do forget their parents and relatives. But is it possible for a husband not to feel sorry at the death of his wife for such a long time? Is he a stone or a man? Does it not seem unrealistic?

ASSIMILATION

When I read "The telegram on the table" I felt that it is my own story. I was always woven (a'g]sf]) a beautiful dream of going overseas and earning a lot of money. But this story has force me to think about my home and family. Then I wonder if I am right in forgetting my past completely. Anyway I have realized my mistakes and now I will try to keep in touch with my village and family.








CHAPTER THIRTY TWO
A PAINFUL CASE

LITERAL COMPREHENSION

Mr. James Daffy, a middle aged bachelor lives an adventure less life in the beginning. But adventure comes when he meets Mrs. Emily Sinico by chance. They see each other at concert and make appointments and finally he visits her regularly at her home. Their friendship grows. He shares his intellectual life with her. She enjoys the break in her solitude (loneliness) but one night she makes the mistake of catching of his hand passionately and pressing it to her cheeks. He leaves her for ever. But four years later, Mr. Duffy reads in the paper of the lady's death. She has been knocked down by a train in a state of intoxication (drunkenness). Mr. Duffy's first reaction is one of hatred at such excessive drunkenness and of self-righteousness. On second thoughts however he feels uneasy and after a fit at self-pity realizes the burden of loneliness.


INTERPRETATION

This story tells as about loveless ness. It describes two painful cases: a man who denies (say "No") love and a woman vainly search for it. It also tells us about loneliness. Lonely people fail to communicate with each other. But they realize the value of love and companionship only when it is very late.

CRITICAL THINKING
The writer has presented the extra married love in this story and laughed at the main character because he refused such love. Living in the conservative Nepali society, we agree with James Duffy, not with the writer. How can we accept the love between married woman and a bachelor? How such a moralist did realized his mistake? How could he reel sorry for Mrs. Sinico?

ASSIMILATION

When I read this story I identified myself with Mrs. Sinico. I do not support her immoral love if she really wanted it. But I support her desire for friendship. Life is really lonely and hard to live if there is no one to love. In such a situation, one must have a friend. Otherwise, one become weak and starts drinking.


CRITICAL THINKING

To do an experiment we can provide the fly with handle by attached it on a stick with wax. Then we can lover it gently over sauces of water until its feet just touch the water if the fly is thirsty, it will lower its proboscis as soon as its feet's touch the water and will suck in keenly. After its thirsty has been reduce it will pull back the proboscis next. We can lower the fly into a saucer of sugared water. It will take out the proboscis again. Then there is plane water the proboscis will be in and when there is sugar water the proboscis will be out.

ASSIMILATION

The fly has a more acute(tLj) sense of taste than human beings. It can taste even the weaker solution than we can taste. It can also distinguish between different kind of sugar. Grave sugar, cane sugar, malt sugar, milk sugar, beat sugar. But it not flood artificial sweetness. The fly knows the different between sweet taste and other kinds of taste. It accepts sweet taste and request other kind of taste. It can find out which sugar solution has more salt touch the sugar water it sucks in the dye





CHAPTER THIRTY THREE
THE LADY WITH THE DOG

LITERAL COMPREHENSION

Gurov saw Anna at Yalta, a seaside town. Both of them had arrived there for their holiday. Anna's husband was expected to join her there. But when he did not come Gurov went to her hotel and made love with her. Anna was sorry for what she had done. Then Gurov consoled and both of them spent the day together, dining, lunching, and visiting places. When Anna got a later from her husband, she went back home. But she told Gurov that she would never visit him. Gurov also went home in Moscow, but he did could not forget Anna. He met her at the theater and she promised to come to Moscow. After this, she would see him in Moscow once in every two or three months. Although they were growing older, they felt that they loved each other more and more. But they were force to live separately. They were planning to live in the same city and see each other openly. But it would be very difficult.

INTERPRETATION

This story might be trying to tell us that true love beginning when people become more experienced and when they have cross the barrier of lust (passion). It may also be interpreted to mean that human beings are puppets in the hand of fate. We do not know whom we love and whom we marry. Anyway, this story stands as a remarkable proof of the writer's belief in the value of human love.

CRITICAL THINKING

This story has beautifully presented the unlawful love of two married persons. Both of them do not love their spouses. But plan to live in the same city seeing each other openly. Will their plan be successful? Will their spouses accept their love? Should they not be punished for their unlawful love? These are some of the question which arias in our minds when we read this story.

ASSIMILATION

After reading this story I realize how important love is in human life. It is the only shelter for human beings. Wealth and education do not makes one's life complete if there is no one to love truly.


CHAPTER THIRTY FOUR
ON THE EVE OF HIS EXECUTION

LITERAL COMPREHENSION

Although young, the poet is very unhappy. There is no sign of happiness. There is only pain. His corn field is full of weeds. He can hope unsuccessfully for batter future. But there is no sign of batter life after waiting for such a long time. Although he is alive he feels that his life has ended. People have heard his story, but nobody has spoken on his behalf. As a young man he could live so many more years, but because of his execution he has loosed everything in life. He is uncared and ignored. Death has followed him from the womb and life has become merely a shade although he has everything necessary for life, he is going to be executed.

INTERPRETATION

This poem expresses the feeling of a healthy person who is going to be executed young. The poet is living the remaining moment of life strongly. The on coming death has made him observe his whole life. He evaluates what life has given him. As his execution is unexpected everything in his life is unexpected and unnatural.


CRITICAL THINKING

This poem has three stanzas. It is an elegy (zf]suLt). It express controlled feeing. It is so well expressed and natural and so skillfully composed that it is regarded as the little master piece in literature. The music of the line is serious but not saddening. The seriousness is emphasized by the repetition of the rhymed refrain as though the poet were expecting the slow tolling of the bell announcing his heath.


ASSIMILATION

When I read this poem I identified my self with the poet. I felt vaguely what a young man feels when he is sure to die. I realized that all my connecting with the world would be cut off if I die soon. I felt a XXXX kind of emptiness in life.


CHAPTER THIRTY FIVE
TO AN ATHLETE

LITERAL COMPREHENSION

One day the young athlete won the race sponsored by competing municipalities. After his victory he was given a public procession and praised through out the town. The whole town proudly watched all this. Next year the young athlete is being carried through the town once again, not for a victory, but for a memorial, along the same route, but this time in a coffin. The home that the athlete is taken to today is his grave. The athlete is praised for his timely death. The athlete is praise because he will know only victory. He will never know how temporary fame is, nor will he feel the pain of fame fading away. The young man will never know the pain of not winning in the same race the next year, and he is always be remembered as a hero by the living. The death hero can never see his record beaten. He is lucky not to be among those who live longer than their achievements. He should be proud of his winning which he will take to the grave with him. He will always be remembered for his success in life which was signified by the garland that he once wore in his hair.

INTERPRETATION

This poem might be trying to tell us that fame is more short-lived than the life itself. So one should try one's best to maintain be honour. It may also be interpreted to mean that one should always live a famous life by sacrificing anything.

CRITICAL THINKING

The speaker has praise the athlete because he died when his name is at the top. But I disagree with the speaker. I think that life is meant to be lived, not no die just for the shake of honour. But if the speaker is consoling the athlete to accept the sure death I agree with him.

ASSIMILATION

By reading this poem I realized how certain death is. One has to die whether one is young or old, whether one is famous or notorious. But it is batter to die young than to live long being notorious.


CHAPTER THIRTY SIX
THE GREAT ANSWER

LITERAL COMPREHENSION

In a French village near the Spanish border, a lot of refugees had gathered. They all wanted to cross the border and sail safely to the USA. If they were cut by the Gestapo, the secret Germen police, they would be either impression or murdered. Among the refugees were a young mother and her 4 years old daughter. They all met at the foot of the mountain. A guide was leading them all. On the way the weakest old man said that he was tired and unable to climb further, but he asked them to leave him there to die. However the guide insists that the old man should keep on climbing with the child on his shoulder until he died. After this two more old man said the same thing, and they also had to carry the child. After they all had crossed the border safely the three old man felt stronger a, freer and livelier than others

INTERPRETAION

This story might be trying to tell us that life is full of struggle and that those who worked harder even at the critical moment are sure to get success. It may also be interpreted to mean that success welcomes those who are never tired of hard labor.

CRITICAL THINKING

This short story has beautifully presented the great answer for the riddle of life. Norman people worded hard but that work harder untiringly enjoy the fruit of hard work batter. If we read this story literally we may disagree with the writer. We wonder how the weakest and oldest man can carry the child, when he himself is unable to word. But there are many moment in our life when even young people like as feel like the three old men. The only solution to our problem at such a moment is to do like the old man .

ASSIMILATION

This story brought a great change in my life. Now my philosophy of life has become to work untiringly. There is no limitation of age for a hard worker. If hard work tries to discourage as , we should do even harder work.

CHAPTER THIRTY SEVEN
A TALE

LITERAL COMPREHENSION

Once upon time, a man went in to the jungle and started penance (tk:of) to win suprime knowledge and godhood. He conquered (lhTof]) his flesh and mind and achieve a state of unending meditative delight. Indra, the king of gods was afraid that the sage might seized his throne through penance. Then he sent a beautiful nymph to destroyed the sage's penance. The attractor posture of he nymph in the river made the sage open his eyes involuntarily. Then both of them married and led a domestic life. They help the needy people in the village. But the villagers were suspicious of him and they always blamed the woman for his downfall, but the sage had the same inner peace even when he was leading the domestic life.

INTERPRETATION

This story might be trying to tell us that after you get suprime knowledge, it is not necessary for you to live in the jungle, and that you will enjoy the same happiness everywhere. It may also be interpreted to mean that to an enlightened person(1fg kfKt JoQmL) the joy derive from any source is similar.

CRITICAL THINKING

For modern people this story is unacceptable from many point of view. Are god there in the heaven? Are god so envious (jealous) of human beings? Are god so helpless that they really need the help of ordinary human beings?




ASSIMILATION

This story reminded me the story of Vishwamitra and Menaka a nymph, had destroyed the penance of the sage Vishwamitra and they had become the parents of Sakuntala. It also convince me how powerful sexual passion is. It never dies. I have understood my own passion batter and tried to use it correctly.






CHAPTER THIREY EIGHT
STOPPING BY WOOD ON A SNOWY EVENING

LITERAL COMPREHENSION

The speaker is returning home at dusk in his one-horse slag. He stops to enjoy the peace and solitude of the occasion: the snow is falling softly, the woods are inviting and there is no other human to break the silence . but the horse find no reason for stopping: it is growing dark there stretch before them. Collecting on his horse's impatience, the speaker admits that he should move on to keep the commitments he has made.

INTERPRETATION

This poem might be trying to tell us that conflict within the man: shall he yield to the temptation of the beautiful woods or move on to the fulfill his promises ? the driver agree to move on because he has promising and responsibilities to fulfill to humanity during the year before he dies. It may also be interpreted to mean that life is a journey full of beauties and duties but one must performed duties ignoring the beauties.

CRITICAL THINKINH

If we interpret the poem literally we can raise many questions. How can a horse think? Can he asked if there is some mistakes? Is he challenging the driver impractical scene when he has stopped without a farmhouse nearby? This poem has four stanzas. The third line of every stanza accept the last one rhymes with three lines of the following stanzas. But in the last stanza there is no new rhyming word , which suggest that the conflict has came to an end.



ASSIMILATION

By reading this poem I came to know that we should keep on performing our duties until we die. There may be many temptations on the way but we must ignore them and move on to our goal.

CHAPTER THIRY NINE
CONTENTS OF THE DEAD MAN'S POCKETS

LITERAL COMPREHENSION

Tom Benecke did not go to the cinema with his wife. Because he wanted to prepare a report for his boss to read at the week end. This report was a path to reach the top in his organization some time in the distant future. when he open the door for his wife to go, a rush of wind drifted the yellow sheet of paper and it slipped out of the window on the ledge of the eleventh story of the building in NewYork. This sheet was necessary to prepare the report and it contented the material he had collected by spending two month. Without thinking seriously, he opened the window forcefully and came out on the narrow ledge. To get the paper he moved side ways along the ledge by holding on to the projected bricks. When he bent down to pick up the paper, he saw the whole city bellow and he almost fainted and fall down. After he picked it up he came back to the window unknowingly. The window was closed and he could not open it. He asked for help, but nobody cared. He could not wait for his wife to return. He had risked his life for a sheet of paper. Finally he broke the window and came in. as he was going to his wife, the paper was drifted again but he laughed at it.

INTERPRETATION

This story might be trying to tell us that ambition is the root of many troubles in life. If people were satisfied with what they got in their life, they would be very-very happy. It may also be interpreted to mean that happy family life is batter than the roll of life.

CRITICAL THINKIGN

This story has clearly expressed the near-death experience of a person. But the behavior of Tom is exaggerated (rflxg] eGbf a9L). how can a person walk on the ledge of the eleventh story? How sane is he? Does ambition make man so mad that he risks his life for such an unimportant thing?

ASSIMILATION

By reading this story I came to know how dangerous ambition is. Although we may not behave like Tom we ignore many risky moment in life. When we are in danger, we realize our foolishness. But the moment we are out of danger,. We forget the risk. This story has clearly brought out human thought less ness.





CHAPTER FORTY
WE ARE BREAKING THE SILENCE ABOUT DEATH

LITERAL COMPREHENSION

Elisabeth Kublor – Rose work with the dying people in the mid 60 's. Before that time the topic to death was banded. Now death has become a fashionable subject. Through her best selling book " on death and dying" she has alert a new way of handling dying. She has suggested that the people should die in their own homes rather than in a strange hospital. After working with the dying people for a long time, she has pointed out five psychological stages people usually experience when they know that they are going to die soon. These stages are denial, anger or rage, bargaining, depression and acceptance. These reaction are not limited to dying but can take place with any change or lost.



INTERPRETATION

The dying person denies or says "No" when he first knows that he is going to die. The denial makes it easy for him to bear the force of death. At the unconscious level, a person never believes that he will die. From their refusal he begins to hope. Kublor Rose suggest that we should take about death with the patient and arrange to complete all possible things.


Assimilation

When a patient stop denying, he begins to be angry. He is angry seeing other healthy people. When his anger becomes less, he starts to bargaining with god. He wants to become good if he is given some more time to live. After he has accepted his death partially, he becomes depressed. He feels sorry for the past mistakes or incomplete tasks. He want to passed time in isolation. Finally he accept death peacefully and he is not worried about making his life longer. He settles everything. His own diseases also does not worry him. He enjoy the present moment without thinking of the future. He lives the full life.

CHAPTER FORTY ONE
FIVE STAGE OF GRIEF BY LINDA PASTAN

LITERAL COMPREHENSION

When the speaker lost her husband, someone suggest that she should go through the five stage of grief. First of them was denial. She denied his absence and gave him the toast and the paper at the breakfast table. But he hide behind the paper. Then she was angry. Therefore she burned to the toast and took the paper from his hand forcefully and start to read it herself. The third stage was bargaining. What could she exchange for him? What would she gain if she remain silent after quarrelling? Before she decided she was depressed (sad). Their relation was poor and weak. Then she hope for improvement but it was useless. Afterward she accepted his loss but she realize that the matter did not end there. It start again because in conjugal life this kind of grief is a repetitive.

INTERPRETATION

This poem might be trying to tell us that the relation between the husband and the wife is always changing. They can not always live happily compromising with the reality. In their life grief is a circular staircase.


CRITICAL THINKING

Linda Pastan has clearly expressed the bitter experience of a married woman when her relation with her husband becomes bad. This poem is in the form of prose (u3). It sound like drama. The speaker is addressing her husband and pouring (vgfpg') her emotions. The poet has use green and neon for "flickering hope."

ASSIMILATION

When I read this poem I came to know more about the life of the married couple. They have almost similar experiences everywhere in the world. This poem also reminded me of Cublor Ross who has charted five psychological stages of grief.

CHAPTER FORTY TWO
WHERE THE MIND IS WITH OUT FEAR

LITERAL COMPREHENSION

The poet imagines the perfect heaven. There people feel no fear and they are equally respected and they can walk raising their heads. There people can get knowledge freely without any disturbances. The world there is no divided in to smaller countries by any kind on narrow border line. People there will speak the truth and work untiringly until they get perfection. There superstition and tradition do not block the region and people always come to the logical conclusion. In such a world of freedom the poet wants god to awalan (wake up) all his countrymen.

INTERPRETATION

This poem might be trying to tell us the value of reason, knowledge, freedom, universality and honesty. The poet may be trying to create some kind of utopia, that is , an ideal and perfect place where everyone lives in harmony and everything is for the best.

CRITICAL THINKING
This is a prose poem. It is read like a conversation. The poet is talking to the almighty father. It may sound idealistic but it is the poet who can imagine a batter world. This king of should our target. We should try to reach it as closely as possible.

ASSIMILATION

This poem has thought be to live a fearless life. It has also inspired me to live a batter life. It has made me forget my present unhappy condition and imagine a utopian world.


New Year – Four Levels of Interactions
Parijat (1934 – 1993)
Translated by Padma Devkota
For: BA / BBS First Year
Literal Comprehension: This poem is composed by Parijat. Here, when the speaker sees the mind that chases March away and the sum which climbs up the hill, she realizes the arrival of the New Year. She can pre-assume that a New Year day has arrived by seeing the nightingale flying here and there, and buds of flowers.
The third stanza begins with “but”, and it shows the contrast in the poet’s thinking. When New Year comes, we expect some new thing but the poet again describes the same old thing. She sees the mason wasps returning lazily to their same old nests, which is in the dark and dirty ceiling of her house. The arrival of New Year should have brought new thing but the mind is busy in same old dreams. Seeing this, she feels to paint the nature afresh.
Interpretation: The poem brings reversal in expectation of the readers. The poem consists of 12 lives. The first six lines describe the changes brought by the arrival of New Year. Then the seventh line begins the contrast but the poem does not include any contrast rather it describes the same old workings. The last two lines show the poet’s desire to rebel against nature.
Critical thinking: The poem teaches a lesson that life without changes has no value. All the routine works are meaningless if there is no change. The poet enjoys the arrival of New Year; but, soon she remembers all her works does not guarantee the changes and freshness in life.
Assimilation: I find the speaker pessimistic towards life. We should have determination. If there is no change after our work and determination, we should understand that our work is not sufficient to bring changes in life. We should take lesson from our part.

No Smoke From The Chimneys – Four Levels of Interactions
For: BA / BBS First Year
Siddhicharan Shrestha (1912 – 1992)
(Translated by Michael Hutt)

Literal Comprehension: The poem “No Smoke from the Chimneys” is written by famous Nepali poet Siddhicharan Shrestha (1912 – 1992) and translated by Michael Hutt into English. In this poem the poet has expressed a freedom fighter as the speaker. The speaker tells that he is busy wiping up blood from a broken head so that Death not to call him. The people who are engaging in the protest against the monopolized political entity are seriously injured, but they are not afraid. The people are not caring to food for freedom and justice; they have no time for cooking. Therefore, nothing including the Lady’s (Death’s) calling can stop the speaker’s advancing feet or distract him from taking part in the protest.
Interpretation: The speaker of this poem may be trying to express that freedom is more important than food or fear of death. Therefore, people do not get diverted or stop when they once have come out of their house to the streets. This poem is all about politics which describes a time when the Nepalese people were fighting for democracy against the Rana regime.
Critical Thinking: While appreciating the speaker’s idea in poem, I did not like the name ‘Lady’ used for death. In our society, the word ‘leady’ means nice and sincere women who deserve respect and value. But the speaker of the poem has shown Death as a beautiful lady. This isn’t quite matching. The title of the poem has unable to reflect the real mood of the speaker.
Assimilation: Now I know how the Nepalese people fought against the autocratic rule for the freedom. The death could not discourage them from establishing democracy in the country. Otherwise, my generation would not have been enjoying the freedom.

Friday, July 10, 2015

BBA First Semester Bsuiness Mathematics Notes of Permutation and Combination



Permutation and combination
Permutation and combination

Basics Concepts and Formulas in Permutations and Combinations

Fundamental Principles of Counting : Multiplication TheoremIf an operation can be performed in m different ways and following which a second operation can be performed in n different ways, then the two operations in succession can be performed in m × n different ways.

Fundamental Principles of Counting : Addition TheoremIf an operation can be performed in m different ways and a second independent operation can be performed in n different ways, either of the two operations can be performed in (m+n) ways.


Factorial:
Let n be a positive integer. Then n factorial (n!) can be defined as

n! = n(n-1)(n-2)...1


Examples:5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6

Special Cases:
a)0! = 1
b)1! = 1

Permutations:
Permutations are the different arrangements of a given number of things by taking some or all at a time

Examples:
a)All permutations (or arrangements) formed with the letters a, b, c by taking three at a time are (abc, acb, bac, bca, cab, cba)

b)All permutations (or arrangements) formed with the letters a, b, c by taking two at a time are (ab, ac, ba, bc, ca, cb)

Combinations:
Each of the different groups or selections formed by taking some or all of a number of objects is called a combination

Examples:Suppose we want to select two out of three girls P, Q, R. Then, possible combinations are PQ, QR and RP. (Note that PQ and QP represent the same selection)

Suppose we want to select three out of three girls P, Q, R. Then, only possible combination is PQR


Difference between Permutations and Combinations and How to Address a Problem
Sometimes, it will be clearly stated in the problem itself whether permutation or combination is to be used. However if it is not mentioned in the problem, we have to find out whether the question is related to permutation or combination.

Consider a situation where we need to find out the total number of possible samples of two objects which can be taken from three objects P,Q , R. To understand if the question is related to permutation or combination, we need to find out if the order is important or not.

If order is important, PQ will be different from QP , PR will be different from RP and QR will be different from RQ

If order is not important, PQ will be same as QP, PR will be same as RP and QR will be same as RQ

Hence,
If the order is important, problem will be related to permutations.
If the order is not important, problem will be related to combinations.

For permutations, the problems can be like "What is the number of permutations the can be made", "What is the number of arrangements that can be made", "What are the different number of ways in which something can be arranged", etc

For combinations, the problems can be like "What is the number of combinations the can be made", "What is the number of selections the can be made", "What are the different number of ways in which something can be selected", etc.

Mostly problems related to word formation, number formation etc will be related to permutations. Similarly most problems related to selection of persons, formation of geometrical figures , distribution of items (there are exceptions for this) etc will be related to combinations.


Repetition:
The term repetition is very important in permutations and combinations.
Consider the same situation described above where we need to find out the total number of possible samples of two objects which can be taken from three objects P,Q , R.

If repetition is allowed, the same object can be taken more than once to make a sample.
i.e., if repetition is allowed, PP, QQ, RR can also be considered as possible samples.

If repetition is not allowed, then PP, QQ, RR cannot be considered as possible samples
Normally repetition is not allowed unless mentioned specifically.

pq and qp are two different permutations ,but they represent the same combination.


Number of permutations of n distinct things taking r at a time:Number of permutations of n distinct things taking r at a time can be given by

nPr = n!(n−r)!=n(n−1)(n−2)...(n−r+1)where 0≤r≤n

If r > n, nPr = 0

Special Case: nP0 = 1

nPr is also denoted by P(n,r). nPr has importance outside combinatorics as well where it is known as the falling factorial and denoted by (n)r or nr

Examples

8P2 = 8 x 7 = 56
5P4= 5 x 4 x 3 x 2 = 120


Number of permutations of n distinct things taking all at a time:

Number of permutations of n distinct things taking them all at a time = nPn = n!

Number of Combinations of n distinct things taking r at a time

Number of combinations of n distinct things taking r at a time ( nCr) can be given by
nCr = n!(r!)(n−r)!=n(n−1)(n−2)
(n−r+1)r!where 0≤r≤n

If r > n, nCr = 0

Special Case: nC0 = 1

nCr is also denoted by C(n,r). nCr occurs in many other mathematical contexts as well where it is known as binomial coefficient and denoted by (nr)

Examples:
1. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?ans) Number of ways of selecting 3 consonants out of 7 = 7C3
Number of ways of selecting 2 vowels out of 4 = 4C2

Number of ways of selecting 3 consonants out of 7 and 2 vowels out of 4 = 7C3 x 4C2
It means that we can have 210 groups where each group contains total 5 letters(3 consonants
and 2 vowels).
Number of ways of arranging 5 letters among themselves = 5!
= 5 x 4 x 3 x 2 x 1 = 120
Hence, Required number of ways = 210 x 120 = 25200


2. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
ans) In a group of 6 boys and 4 girls, four children are to be selected such that
at least one boy should be there.
Hence we have 4 choices as given below

We can select 4 boys ------(Option 1).
Number of ways to this = 6C4

We can select 3 boys and 1 girl ------(Option 2)
Number of ways to this = 6C3 x 4C1

We can select 2 boys and 2 girls ------(Option 3)
Number of ways to this = 6C2 x 4C2

We can select 1 boy and 3 girls ------(Option 4)
Number of ways to this = 6C1 x 4C3

Total number of ways
= (6C4) + (6C3 x 4C1) + (6C2 x 4C2) + (6C1 x 4C3)
= (6C2) + (6C3 x 4C1) + (6C2 x 4C2) + (6C1 x 4C1) [Applied the formula nCr = nC(n - r) ]
= 15 + 80 + 90 + 24
= 209


3. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
ans) From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
Hence we have the following 3 choices

We can select 5 men ------(Option 1)
Number of ways to do this = 7C5

We can select 4 men and 1 woman ------(Option 2)
Number of ways to do this = 7C4 x 6C1

We can select 3 men and 2 women ------(Option 3)
Number of ways to do this = 7C3 x 6C2

Total number of ways
= 7C5 + [7C4 x 6C1] + [7C3 x 6C2]
= 7C2 + [7C3 x 6C1] + [7C3 x 6C2] [Applied the formula nCr = nC(n - r) ]
= 21 + 210 + 525
 = 756


4. In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?ans) The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels
should always come together. Hence these three vowels can be grouped and considered as a
single letter. That is, PTCL(OIA).

Hence we can assume total letters as 5. and all these letters are different.
Number of ways to arrange these letters = 5! = [5 x 4 x 3 x 2 x 1] = 120

All The 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves = 3! = [3 x 2 x 1] = 6

Hence, required number of ways = 120 x 6 = 720


5. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?ans)The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and
these 5 vowels should always come together. Hence these 5 vowels can be grouped
and considered as a single letter. that is, CRPRTN(OOAIO).

Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and
rest of the letters are different.

Number of ways to arrange these letters = [Loading Maths... ]2520In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.

Hence, required number of ways = 2520 x 20 = 50400


6. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?ans)We need to select 5 men from 7 men and 2 women from 3 women

Number of ways to do this
= 7C5 x 3C2
= 7C2 x 3C1 [Applied the formula nCr = nC(n - r) ]
= 21 x 3
 = 63


7. In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
ans) The word 'MATHEMATICS' has 11 letters. It has the vowels 'A','E','A','I' in it and
these 4 vowels must always come together. Hence these 4 vowels can be grouped and
considered as a single letter. That is, MTHMTCS(AEAI).

Hence we can assume total letters as 8. But in these 8 letters, 'M' occurs 2 times,
'T' occurs 2 times but rest of the letters are different.


Hence,number of ways to arrange these letters = [Loading Maths... ]In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.
Hence, required number of ways = 10080 x 12 = 120960


8. There are 8 men and 10 women and you need to form a committee of 5 men and 6 women. In how many ways can the committee be formed?
ans)We need to select 5 men from 8 men and 6 women from 10 women

Number of ways to do this
= 8C5 x 10C6
= 8C3 x 10C4 [Applied the formula nCr = nC(n - r) ]
= 56 x 210
= 11760


9. How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?ans)The word 'LOGARITHMS' has 10 different letters.

Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 10P3
= 10 x 9 x 8
= 720

10. In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
ans) The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and
these 3 vowels should always come together. Hence these 3 vowels can be grouped
and considered as a single letter. that is, LDNG(EAI).

Hence we can assume total letters as 5 and all these letters are different.
Number of ways to arrange these letters = 5! = 5 x 4 x 3 x 2 x 1 = 120

In the 3 vowels (EAI), all the vowels are different.
Number of ways to arrange these vowels among themselves = 3! = 3 x 2 x 1= 6

Hence, required number of ways = 120 x 6= 720











Domain and Range

Domain and Range of a Function

Domain:The domain of a function is the complete set of possible values of the independent variable.
ie;The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

When finding the domain, remember:
The denominator (bottom) of a fraction cannot be zero.
The number under a square root sign must be positive in this work
eg:
Here is the graph of y=√​x+4​​​:

http://intmstat.com/functions-and-graphs/domain.gif

The domain of this function is x≥−4, since x cannot be less than −4. To see why, try out some numbers less than −4 (like −5 or −10) and some more than −4 (like −2 or 8) in your calculator. The only ones that "work" and give us an answer are the ones greater than or equal to −4. This will make the number under the square root positive.

Notes:
The enclosed (colored-in) circle on the point (−4,0). This indicates that the domain "starts" at this point.

How to find the domainIn general, we determine the domainof each function by looking for those values of the independent variable (usually x) which we are allowed to use. (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign).

Range:The range of a function is the complete set of all possible resulting values of the dependent variable (y,usually), after we have substituted the domain.
ie;The range is the resulting y-values we get after substituting all the possible x-values.
How to find the range:
The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is yalways positive? Always negative? Or maybe not equal to certain values?)
Make sure you look for minimum and maximum values of y.
Draw a sketch! In math, it's very true that a picture is worth a thousand words.
Some Questions:
a) f(x)=x^​2​​+2 Domain: The function f(x) = x^2 + 2 is defined for all real values of x (because there are no restrictions on the value of x).

Hence, the domain of f(x) is"all real values of x".

Range: Since x^^2 is never negative, x^2 + 2 is never less than 2
Hence, the range of f(x) is"all real numbers f(x)≥2".

We can see that x can take any value in the graph, but the resulting y = f(x) values are greater than or equal to 2.

http://intmstat.com/functions-and-graphs/x2plus2.png



(b) f(t)=​1/t+2​​
Domain: The function f(t)=1/​t+2​​ is not defined for t = -2, as this value would result in division by zero. (There would be a 0 on the bottom of the fraction.)

Hence the domain of f(t) is"all real numbers except -2"

Range: No matter how large or small t becomes, f(t) will never be equal to zero.
 If we try to solve the equation for 0, this is what happens:
0=​t+2​​1​​

Multiply both sides by (t + 2) and we get
0=1

This is impossible.So the range of f(t) is"all real numbers except zero".

We can see in the graph that the function is not defined for t=−2 and that the function (the y-values) takes all values except 0.

http://intmstat.com/functions-and-graphs/1ontplus2.png



C)
State the domain and range of the following relation. Is the relation a function?
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}


The above list of points, being a relationship between certain x's and certain y's, is a relation. The domain is all the x-values, and the range is all the y-values. To give the domain and the range, I just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(It is customary to list these values in numerical order, but it is not required. Sets are called "unordered lists", so you can list the numbers in any order you feel like. Just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

While the given set does represent a relation (because x's and y's are being related to each other), they gave me two points with the same x-value: (2, –3) and (2, 3). Since x = 2 gives me two possible destinations, then this relation is not a function.

Note that all I had to do to check whether the relation was a function was to look for duplicate x-values. If you find a duplicate x-value, then the different y-values mean that you do not have a function.

D)State the domain and range of the following relation. Is the relation a function?
{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}


I'll just list the x-values for the domain and the y-values for the range:

domain: {–3, –2, –1, 0, 1, 2}
range: {5}
This is another example of a "boring" function, just like the example on the previous page: every last x-value goes to the exact same y-value. But each x-value is different, so, while boring, this relation is indeed a function. In point of fact, these points lie on the horizontal line y = 5.

There is one other case for finding the domain and range of functions. They will give you a function and ask you to find the domain (and maybe the range, too). I have only ever seen (or can even think of) two things at this stage in your mathematical career that you'll have to check in order to determine the domain of the function they'll give you, and those two things are denominators and square roots.


E)Determine the domain and range of the given function:
http://www.purplemath.com/modules/fcns/domain04.gif

The domain is all the values that x is allowed to take on. The only problem I have with this function is that I need to be careful not to divide by zero. So the only values that x can not take on are those which would cause division by zero. So I'll set the denominator equal to zero and solve; my domain will be everything else.

x^2 – x – 2 = 0
(x – 2)(x + 1) = 0
x = 2 or x = –1

Then the domain is "all x not equal to –1 or 2".

The range is a bit trickier, which is why they may not ask for it. In general, though, they'll want you to graph the function and find the range from the picture. 
In this case: 
http://www.purplemath.com/modules/fcns/domain01.gif


As I can see from my picture, the graph "covers" all y-values (that is, the graph will go as low as I like, and will also go as high as I like). Since the graph will eventually cover all possible values of y, then the range is "all real numbers".


F)Determine the domain and range of the given function:

http://www.purplemath.com/modules/fcns/domain05.gif

The domain is all values that x can take on. The only problem I have with this function is that I cannot have a negative inside the square root. So I'll set the insides greater-than-or-equal-to zero, and solve. The result will be my domain:

–2x + 3 > 0
–2x > –3
2x < 3
x < 3/2 = 1.5

Then the domain is "all x < 3/2".

The range requires a graph. I need to be careful when graphical radicals.
http://www.purplemath.com/modules/fcns/domain02.gif


The graph starts at y = 0 and goes down from there. While the graph goes down very slowly, I know that, eventually, I can go as low as I like (by picking an x that is sufficiently big). Also, from my experience with graphing, I know that the graph will never start coming back up. Thenthe range is "y < 0".


G)Determine the domain and range of the given function:
y = –x^4 + 4

This is just a garden-variety polynomial. There are no denominators (so no division-by-zero problems) and no radicals (so no square-root-of-a-negative problems). There are no problems with a polynomial. There are no values that I can't plug in for x. When I have a polynomial, the answer is always that the domain is "all x".

The range will vary from polynomial to polynomial, and they probably won't even ask, but when they do, I look at the picture:
http://www.purplemath.com/modules/fcns/domain03.gif

The graph goes only as high as y = 4, but it will go as low as I like. Then:

The range is "all y < 4".

BBA II Semester English Notes

CHAPTER TWENTY HOW SANE ARE WE? LITERAL COMPREHENSION The concept of wise and good rulers is merely imaginary. In fact, our colle...