Consider this function defined by an integral: f(x) = f* arctan(3t) t 0 (a) Find the power series representation centered at x = 0. Complete the given equation. Answer: f(x) = Σ 71=0 dt. (b) Enter the first 5 nonzero terms of the power series.

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.
Chapter8: Further Techniques And Applications Of Integration
Section8.4: Improper Integrals
Problem 12E
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Consider this function defined by an integral:
ƒ(x) = f* * arctan(3t) dt.
t
(a) Find the power series representation centered at x = 0. Complete the given equation.
Answer: ƒ(x) =
Answer: f(x) =
∞
(b) Enter the first 5 nonzero terms of the power series.
n=0
Answer:
+
+
(c) Find the interval of convergence for the power series. Answer in interval notation.
+
Transcribed Image Text:Consider this function defined by an integral: ƒ(x) = f* * arctan(3t) dt. t (a) Find the power series representation centered at x = 0. Complete the given equation. Answer: ƒ(x) = Answer: f(x) = ∞ (b) Enter the first 5 nonzero terms of the power series. n=0 Answer: + + (c) Find the interval of convergence for the power series. Answer in interval notation. +
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