GoodmanW98T4

GoodmanW98T4 - . 8 x 1 . 2. 5. [10 points] Find the Taylor...

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Math 21H Apr. 21, 1998 Test #4 Name: Read each question carefully, and be sure to show clearly how you got your answers as well as what your answers are. 1. [10 points] Find a function f ( x ) such that f 0 ( x )=( xf ( x )) 2 and f (1) = - 3. 2. [10 points] Find the area of the surface obtained by rotating the curve y = x 2 , for 0 x 1, around the y -axis. 3. [10 points] Find the Maclaurin series for the function f ( x )= 1 1+3 x and determine its interval of convergence. 4. [15 points] (a) Approximate f ( x )=1 /x by a Taylor polynomial with degree n = 3 centered at a = 1; and (b) use Taylor’s formula to estimate the accuracy of this approximation for
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Unformatted text preview: . 8 x 1 . 2. 5. [10 points] Find the Taylor series centered at a = 2 for the function f ( x ) = e x . 6. [15 points] Use a power series to approximate Z . 5 1 1 + x 3 dx accurate to four decimal places. 7. [10 points] Write an integral for the length of the curve y = cos x with 0 x , but do not evaluate the integral. 8. [10 points] Find the centroid of the region bounded by y = e x , y = 0, x = 0, and x = 1. 9. [10 points] If f ( x ) = e 2 x cos x , use power series to nd f (4) (0)....
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This note was uploaded on 01/24/2011 for the course MATH 21 taught by Professor Mathdep during the Winter '98 term at Missouri S&T.

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