Southeast Missouri State University Calculus Questions

DescriptionMA145 Test 4
Name
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I. Find radius of convergence and the interval of convergence
∑∞ (−1)n xn
.
1
n2 5 n
2
x
and
II. Find the power series representation for the function f (x) = 1+x
determine the interval of convergence.
III.∫ Use the formula to find the Maclaurin series for g(x) = tan−1 (x2 ), then
find g(x)dx, and d(g(x))/dx as series.
IV. Use definition to find the Taylor series for f (x) = sin(x) at x = 0.
V. Find the sum of the series 1 − ln 2 +
1
(ln 2)2 (ln 2)3

+ ···
2!
3!

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