13) Let f(x) = 4+4x x Compute f(x), f'(x), f'(x), f'''(x), f(iv) (x), f(v) (x) S f(), f'(), f), F" (), Fam داد We see that the first term does not fit a pattern, but we also see that f(k) (1) = 127 for k>1. Hence we see that the Taylor Series for f centered at I is given by [27 f(x) = 8+ 2/² (x-1) k K=1 6-X 10

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 48CR
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13) Let f(x) = 4+4x
X
Compute f(x), f'(x), f''(x), f'''(x), f(iv) (x), f(v) (x)
f(1), f'(1), f"(1), f" (1), flm (1), f^) (1)
We see that the first term does not fit a pattern, but
we also see that f(k) (1) = 127 for k>1.
Hence we see that the Taylor Series for f centered at I
is given by 127
f(x) = 8 + 2² I
(x-1) k
K=1
Transcribed Image Text:Ler 13) Let f(x) = 4+4x X Compute f(x), f'(x), f''(x), f'''(x), f(iv) (x), f(v) (x) f(1), f'(1), f"(1), f" (1), flm (1), f^) (1) We see that the first term does not fit a pattern, but we also see that f(k) (1) = 127 for k>1. Hence we see that the Taylor Series for f centered at I is given by 127 f(x) = 8 + 2² I (x-1) k K=1
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