# 242hw10 - that to the answer Maple(or a calculator gives...

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Math 242 Homework 10 Sections 012 and 014: Due Wednesday May 4th Section 050: Due Tuesday May 3rd 1. Express the indeﬁnite integral Z e x - 1 x dx as a power series. 2. Express the deﬁnite integral Z 0 . 2 0 1 1 + x 5 dx as an inﬁnite series. Then ﬁnd the sum of the ﬁrst two terms of that series. Compare that to the value of the integral that Maple gives you. 3. Find the ﬁrst three terms of the Taylor series for the function f ( x ) = (1+ x ) 1 / 3 . Use those ﬁrst three terms to get an estimate for 1 . 06 1 / 3 . Compare
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Unformatted text preview: that to the answer Maple (or a calculator) gives you. 4. Consider the parametric curve x = sin t , y = csc t , where 0 < t < π/ 2. Eliminate the parameter to ﬁnd a Cartesian equation for the curve. Sketch the curve, and use an arrow to indicate the direction traveled when t increases. 5. (Slightly tricky) With the help of partial fractions, come up with a power series representation for the function f ( x ) = 3 x 2-x-2 . 1...
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## This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.

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