Change of sign method Essay Example for Free

Change of sign method Essay I use the same method to keep doing decimal research. to work out a more accurate answer. Take increments in size 0. 1 within the interval [1. 5,1. 6] From the above we can see that must lie between [1. 52,1. 53]. It can be very clear if I use graph. I will do a better research this time by using the same method to prove my result is correct. Now I can find a more accurate result from the research which lies between [1. 521,. 1522]. Here is a graph to prove the interval is right. However, I will take 4 decimal places to improve the accuracy of the interval. Also I will use the same method again. As we can see the root is between [1. 5213,1. 5214] Same again. Autograph is used to prove my solution is right. Error bounds This is the process which check how the accuracy of the roots are. From those 4 decimal search I have done so far, I can say that the answer is between 1. 5213 and 1. 5214. These can be improved the accuracy. Assume X=1. 5213 f(x)=(1. 5213)^3-1. 5213-2=-0. 00047 X=1. 5214 f(x)=(1. 5214)^3-1. 5214-2=0. 000121 Because the answer is -0. 0004700. 000121. So the answer must between 1. 5213 and 1.5214. However , these are not the exact answer so I have to estimate them. In this case, X=1. 5213. 5, so the error bound is . Because this is the middle point between the interval. Fail example by using Exel It is not guaranteed to use this method, because there still has some problems in it. See the graph below: As we can see the curve touches the x axis. The root lies between 0 and 1. I am going to use Exel program to prove it. There is no change of sign of this equation. So we can say that the change of sign method is failed. Newton-Raphson method This is another fixed point estimation method, and as for the previous method it is necessary to use an estimate of the root as a starting point. The process can be repeated to give a sequence of points x2, x3 I am going to use the following equation. As we can see there are 2 roots in this function. The first root lies close to +1. But I will estimate the first root is x1 = +2. I will show it in graphical as +2 is a starting point. There is a technical way to do Newton-Raphson method by using Autograph. I will do it step by step with showing the graph. I click the curve then right click it and chook the Newton Raphson Iteration option. I have entered the value that I estimated, then press the right side button. The solutions appear automatically. The answer that I got is 1. 27202. Error bound Because my solution is 5. bp. So the answer will be x=1. 27202 The numbers that I squared shows how close to the real answer. So we can say there are some error in it. I am going to try another root of the equation. I have estimated the x1 = -2. As I can see from the graph, -1. 27202 is the best answer I can get. Then I will check whether the solutions are correct.

Reason to Quit Smoking Essay -- Tobacco Nicotine Smoking Cigarettes

As many know that the effects on people caused by smoking it crossing the final borders of danger to quit that sickening habit of smoking. Hence if I get a chance to ban anything in the world, it will be smoking. Millions of people around the world enjoy the disgusting habit of smoking. This habit contributes to an outbreak of diseases which brings pain, suffering and death to millions every year. We should end this suffering by prohibiting smoking in all its forms. Smokers, non-smokers, and the environment are all adversely affected by smoking. Smoking is one of the worst things you can do to your body. The list of additives allowed in the manufacture of cigarettes consists of 600 possible ingredients. When burned, cigarette smoke contains over 4000 chemicals, with over 40 of them being known carcinogens. Arsenic, carbon monoxide, methanol, cadmium, and hydrogen cyanide are just a few of the ingredients found in today's cigarettes. Some other ingredients include rat poison, lighter fluid, paint stripper, and tar. Studies show that smokers are much more likely to die premature...

Spanish and Italian Borrowings to the English Language

Romanic languages, group of languages belonging to the Italic subfamily of the Indo-European family of languages. They are spoken by about 670 million people in many parts of the world. Among the more important Romanic languages are Catalan, French, Italian, Portuguese, Romanian, and Spanish. My report is particularly about Italian and Spanish borrowings to the English language. Spanish borrowings appeared in English in 16 century. Historic circumstances which influenced on these borrowings are associated with some geographic discoveries at that time.There was a colonization of the South and North America by the Spanish. So the close cooperation with Spain contributed to the developing of borrowings from Spanish into English language. In 16 century close political and economic ties of England with Spain and of Spain with France led to borrowings both directly from Spanish and through the French language. In the beginning of the 16th century there were many Spaniards in England due to dynastic relations between England and Spain. So England inherited many Spanish words which related to Spanish manners. Associated essay: Reasons for Failure in English LanguageMany Spanish words have come to us from three primary sources: many of them entered American English in the days of Mexican and/or Spanish cowboys working in what is now the U. S. Southwest. Some words were borrowed with the Spanish culture-dances and musicals instruments. Words of Caribbean origin entered English by way of trade. The other major source is the names of foods whose names have no English equivalent, as the intermingling of cultures has expanded our diets as well as our vocabulary. There are the following semantic groups: ) trade terms: cargo- , embargo- , contraband-; b) names of dances and musical instruments: tango, rumba, habanera, guitar; c) names of vegetables and fruit: banana, cocoa , chocolate, cigar, cork – , , potato, tobacco, tomato. All of these were the objects of trade. They were borrowed from Spain to England. Anglo-Spanish War also greatly enlarged the vocabulary of English language which included such military terms: galleon – , , guerilla – .Besides during the Renaissance period the whole layer of everyday Spanish words came to the English language. For ex: bravada – , canoe – , , Negro – , ranch – , desperado – , , peccadillo – . In XIX century many borrowings from Spanish were brought through American literature. Such words as: cigarette, lasso, mustang – . There are following words among the recently borrowed ones: macho, amigo, gringo – .As we see, the majority of borrowings from Spanish retain their shape and are commonly used in English in the stylistic purposes to give the narration some Spanish shade. Of course it makes our speech more interesting and shows that we are culturally enriched. For example, we can say â€Å"adios† instead of â€Å"bye† to diversify our communication. English| Spanish| Alcove| Alcoba| Alfalfa| Al falfa| Artichoke| Alcarchofa| Apricot| Albaric oque| Calibre| Calibre| | Armada| Armado| Apricot| Albaricoque|Binnacle| Bitacula| The Italian language had the strongest influence on the English language in the Renaissance period. The art and literature had the great importance for the whole European culture. Italy was the leading country in the economic, politic, cultural fields, so familiarity with the rich Italian literature of this period, painting, sculpture and architecture, traveling to Italy, an interest in the country itself, was reflected in the loans from the Italian language.We should notice that, due to the wide spread of Italian debt in the European languages , some Italian words were borrowed to the English language, not directly but through other languages. Most of the Italian words was borrowed through French. And only in the XVI century, the borrowings were directly from the Italian language. The earliest borrowings related to trade and military affairs. There were borrowed the following words from the field of commerce and finance: ducat – coin, million – million, lombard – pawnshop, bank – bank.From the field of military: alarm – alarm, brigand – bandit, bark – bark, colonel – Colonel, squadron – squadron, sentinel – guard, pistol – gun. The greatest number of words borrowed from Italian related to the field of art, literature, music, theater and architecture. For example, canto – song, sonnet – a sonnet, stanza – stanza, slogan, model – model, miniature – miniature, madonna – Madonna, fresco – fresco, balcony – balcony, mezzanine – mezzanine, mezzanine and so on.Especially a lot of borrowing were from the field of music, such as: – The names of musical instruments: piano, violin, piccolo; – The name of singing voices: bass, baritone, alto, soprano; – The name of music: opera, sonata, aria. Among the 20-th century Italian borrowi ngs we can mention : gazette, incognitto, autostrada, fiasco, fascist, dilettante, grotesque, graffitti etc. We should be notice that there are used even whole phraseological combinations in English, for example, sotto voce – whisper.

The Man And The Monster - 1072 Words

The Man and The Monster Throughout history, there have been many different myths and folklore about monsters. These stories have been passed down many generations and have managed to survive through time, with very little changes. Monsters were created to warn people about the dangers of the unknown in the world. Many of the Monsters have human qualities, both good and bad, imbedded in their being. The similarities between the human and the monster indicate that humans have the capability to be their own monster. Robert Stevenson story, The Strange Case of Dr. Jekyll and Mr. Hyde, demonstrates perfectly that a person has the capability into becoming a monster to society in the story. Despite Dr. Jekyll being a wealthy esteemed member of society, he still became Mr. Hyde, a monster. The undeniable shared characteristics between humans and monsters support the idea that humans will be the destruction of society, if we don’t conform to society’s norms. In most of myths and folklore, monsters contradict society’s rules and ideas of how things should be. For example, vampires are more sexual and werewolves are more primal. Dr. Jekyll became a monster when he decided to be different from society. Mr. Hyde was created because Dr. Jekyll wanted to do something unknown to society. What qualities did Mr. Hyde have that made him a monster? â€Å"Scholars who study monstrosity broadly agree that a monster is something existing near or outside the farthest outlier of acceptable humanShow MoreRelatedThe Man and the Monster in Frankenstein by Mary Shelley Essay1236 Words   |  5 Pages In pursuit of knowledge, he becomes completely absorbed and creates what he calls a â€Å"demonical corpse†; several of the traits that the monster has acquired are a result of his deformities. For example, he has become isolated because others find him hideous, and for that reason he retreats to nature where no one can judge him. 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In the 1960s an English company called Hammer Horror revitalised Frankenstein movies and Christopher Lee made the monster look more like a man. All of the Frankenstein movies before Kenneth Branaghs version had made the monster evil. In Kenneth Branaghs version of the story he filmed the entire book and tried to stick closelyRead MoreAlexandra Giambruno. Mrs.Schroder. English Iv Honors. 231030 Words   |  5 Pages The story of Frankenstein has mysterious aspects that help the main character Victor create the monster. In a gothic novel, there are a ton of abstract thoughts that can be in play pertaining to the type of story that the author creates. Power and Constraint is one point that plays a lot in the novel itself, it all started with the main creator. Victor Frankenstein had the idea to create a monster; he collected body parts and used modern technologies to make an unnatural creature. The novel itself