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 < / 2. Eliminate the parameter to nd 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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