# hw10 - (a Z e x-1 x dx(b Z cos x-1 x dx 6 Find the Taylor...

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MATH 138: Calculus 2 Assignment #10 Due: 12:30 p.m., Monday, December 6 Fall 2010 1. Use power series to evaluate the limit. (a) lim x 0 sin x - x x 3 (b) lim x 0 1 - cos x 1 + x - e x 2. Suppose that f ( x ) = n =0 c n x n for all x . Show that if f is an odd function, then c 0 = c 2 = c 4 = · · · = 0 . (Note: a function f ( x ) is called odd if f ( - x ) = - f ( x ) for all x .) 3. Let f ( x ) = e x 2 . Show that f (2 n ) (0) = (2 n )! n ! for all n = 0 , 1 , 2 , . . . . 4. If f ( n ) (0) = ( n + 1)! for n = 0 , 1 , 2 , . . . , find the Maclaurin series for f and its radius of convergence. 5. Evaluate the indefinite integral as a power series
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Unformatted text preview: (a) Z e x-1 x dx (b) Z cos x-1 x dx 6. Find the Taylor polynomial T 3 ( x ) for the function f at the number a . (a) cos x ; a = π 2 (b) f ( x ) = 1 x ; a = 2 . The following problems are only recommended, not for submission. • Course Notes: All examples in section 5.4. • Stewart: Section 11.9 Exercises 13, 15, 17, 47, 55, 57, 58....
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