University of Washington Differentiable Function Calculus Questions # 11, 13 & 15 Do not write your answers in series notation, Instead, write out the firs

University of Washington Differentiable Function Calculus Questions # 11, 13 & 15 Do not write your answers in series notation, Instead, write out the first four or five terms. Please see attached. nials, then
vision we require bo
Maclaurin series. [Assume that f has a power series expansion.
5-10 Find the Maclaurin series for f(x) using the definition of a
Do not show that R. (.x) – 0.] Also find the associated radius of
formula for bs.
convergence.
5. f(x) = (1 – x)-2
6. f(x) = ln(1 + x)
8. f(x) = cos 3x
7. f(x) = sin 7x
10. f(x) = xe*
9. f(x) =
11-18 Find the Taylor series for f(x) centered at the given value
of a. [Assume that f has a power series expansion. Do not show
that R,(x) →0.]
11. f(x) = x4 – 3×2 + 1, a = 1
1) +
12. f(x) = x – x?, a = -2
13. f(x) = e”, a = 3
14. f(x) = 1/x, a = -3
2) +
15. f(x) = cos x, a = 7
17. f(x) = 1/77, a=9
16. f(x) = sin x, a = 7/2
18. f(x) = x-?, a = 1
Maclaurin
19. Prove that the series obtained in Exercise 7 represents sin ix
for all x.
s?
20. Prove that the series obtained in Exercise 16 represents sin x
for all x.
uired
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