3 2 4 3 5 1 1 1 1 1 + + + k 2 k k 1 k+1 k 1 1 1 = 1+ + 2 k+1 k+2 1 ! 3 2 k X 1 n 1 n+2 1 k+2 so that k X 1 1 = lim n (n + 2) k!1 n=1 n (n + 2) n=1 1 X = lim k!1 1 1 + k+1 k+2 = 3 2 1 3. (18 pts.) Find the Taylor series for f (x) = ln x at x = 4. Determine its interval of convergence. Solution: Recall that 1 X n tn = = = 1 1 t ; n=0 1 X jtj < 1 jtj < 1 jtj < 1 ( 1) tn n=0 1 X ( 1)n tn+1 n+1 n=0 1 ; 1+t ln (1 + t) ; let x
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Astronomy (Jyothissaasthram) was popular in Kerala even in ancient times‚ and their deep knowledge in that branch of science is well-known. A number of great treatises (Grantham) were written by several eminent scholars (most of them Namboothiri Brahmins) of the area at different times. It is difficult to date some of the very ancient ones such as "Devakeralam"‚ "Sukrakeralam" (also known as "Bhrigukeralam"‚ "Kerala Rahasyam" or "Keraleeyam" and has 10 chapters)‚ "Vararuchi Keralam” and "Keraleeya
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sizes too small." The Grinch lies at the peak of Mount Crumpit‚ which looks over the cheerful town of Who-ville‚ filled with the many caring citizens who are eager for Old Saint Nick to arrive soon. Baffled by the thought of someone hating Christmas‚ Taylor Momsen plays the role of a curious young girl‚ Cindy Lou Who‚ that wants to get to know the humble heart of the Grinch for herself. As she begins to talk to the cold hearted Grinch‚ he gets the repulsive idea to steal Christmas this year. Dressed
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Max Weber and Frederick Taylor Weber’s Bureaucratic Theory – the essence of the modern traditionally managed organization. Bureaucracies are arrangements of formal positions. Each position is defined by its specialized duties for which employees are selected on the basis of their technical expertise. Positions are divided (division of labor) into line (positions directly involved in production of goods or services) and staff (positions which advise line and engage
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recapture his glory days of high school sports by leaping hurdles on a track field‚ dreaming about his moments as a youthful athlete. Unexpectedly‚ he falls‚ leaving him dependent on a crutch. Brick‚ along with his wife‚ Maggie "the Cat" (Elizabeth Taylor)‚ are seen the next day visiting his family in Mississippi‚ waiting to celebrate Big Daddy’s (Burl Ives) 65th birthday. Depressed‚ Brick decides to spend his days inside drinking while resisting the affections of his wife‚ who taunts him about the
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U.S. HISTORY (AP) CHAPTER 17 MANIFEST DESTINY AND ITS LEGACY 1. Explain the phrase “Tyler became a president without a party‚ and the Whigs lost the presidency without losing an election.” Tyler’s enemies accused him of being a Democrat in Whig clothing‚ but this charge was only partially true. The Whig party‚ like the Democratic party‚ was something of a catchall‚ and the accidental president belonged to the minority wing‚ which embraced a number of Jeffersonian states’ righters. Tyler
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Hi Peg: Very few comments and very few corrections—mostly punctuation. I have indicated them in red—see check marks in margin. I would have made two simple changes in Taylor Hunts’ excerpt; however I figure it was a direct quote from his book. Love mom The Introduction The three body types‚ or doshas‚ in Ayurveda are Vata‚ Pitta‚ and Kapha. Though we are [I would eliminate the word all here‚ but you don’t have to →] all made up of all three‚ a tendency towards one is common. This tendency can
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The Andy Griffith Show was a sitcom in 1960s and has influenced other family sitcoms alike. On the fifth season of the Andy Griffith show‚ Aunt Bee gets a mysterious letter from‚ “a boy I used to keep company with‚” (1964)‚ he comes to visit and Andy is annoyed by him. The purpose of this paper is to analyze the‚ “Aunt Bee’s Romance” episode on the Andy Griffith show‚ from a critical studies perspective. I argue that the Andy Griffith show’s episode‚ “Aunt Bee’s Romance”‚ Andy reaffirms his masculinity
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be forgotten on enemy lines of independence‚ did Taylor know that? Negatively speaking Taylor lacks the mental capacity to commit to Jax. Call it odd or the way Taylor was raised‚ she treats Jax as an unnecessary luxury. Men like to feel needed and his continuous unrequited feelings for Taylor aren’t exactly beneficial to Jax’s needs. So‚ what does Jax do in ways of self destructing actions‚ he cheats on Taylor? In my opinion its Taylors independence is a brick-wall she constantly puts up
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The presidency of James Knox Polk was a memorable one. He was known as America’s first dark horse candidate‚ and later he was called the only strong commander in chief between Andrew Jackson and Abraham Lincoln (Greenstein 14). Yet‚ many historians still write him off but he was by no means insignificant. Now‚ he may have not been as charismatic as Roosevelt or Reagan but charisma does not mean greatness. Polk was without questions one of the most ambitious and successful presidents in history. In
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