# A10 - listed in the on the Schedule and exercise list sheet...

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MATH 138 Winter 2011 Assignment 10 Topics: Representation of a function as a power series, Taylor and Maclaurin series. Due: 11 a.m. Friday, March 25. Instructions: Print your name and I.D. number at the top of the ﬁrst page of your solutions, and underline your last name. Submit your solutions in the same order as that of the questions appearing herein. On collaboration: First attempt the questions on your own, but if you get help or collaborate with someone, then acknowledge the names of those who helped you. Any outright copying of assignments will be reported as an act of academic plagiarism. On work presentation: Your solutions must have legible handwriting, and must be presented in clear, concise and logical steps that fully reveal what you are doing. Questions such as those to be handed in, as well as those that are recommended, may appear on exams. To avoid frustration and disappointment, get started on your assignment early. Do not forget to work on the recommended problems from Stewart’s book that are

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Unformatted text preview: listed in the on the Schedule and exercise list sheet found on the ACE webpage. This will give you much needed practice. Hand in your solutions to the following problems. Hand in Maple lab # 2 along with this assignment. 1. Find a power series representation for the functions and determine the radius of convergence. (a) ln( x 2 + 4) (b) x 2 ( a 3-x 3 ) 2 1 2. Show that the function f ( x ) = ∑ n ≥ x n n ! is a solution to the differential equation f ( x ) = f ( x ) . 3. Use a power series to approximate the deﬁnite integral R 1 10 1+ x 1-x dx with error less than 10-5 . 4. Compute the Taylor series of sin( x ) centered at π 2 . 5. Use series to evaluate the limit lim x → x-arctan( x ) x 3 . 6. Find the Maclaurin series of f ( x ) = sinh( x ) and prove that it converges to f ( x ) for all x . (Note: if you do not know sinh( x ) , search for hyperbolic functions in the index of the book.) 2...
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## This note was uploaded on 07/24/2011 for the course MATH 138 taught by Professor Anoymous during the Winter '07 term at Waterloo.

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A10 - listed in the on the Schedule and exercise list sheet...

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