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Category > Calculus Posted 10 Jul 2017 My Price 10.00

Homework Sheet 4

Homework Sheet 4
Due: July 7, 2017
The following questions are from chapter 6 of the OpenStax Calculus textbook. The
problem number from the book is listed in parenthesis.
P
n
1. (4) True or false: If ∞
R > 0 and if |bn | ≤ |an | for
n=1 an x has radius
P of convergence
n
all n, then the radius of convergence of ∞
b
x
is
greater
than or equal to R. (Hint:
n=1 n
consider The Direct Comparison Test.) P an+1 an xn
2. (8) Suppose that limn→∞ an = 1. Find the radius of convergence of ∞
n=0 2n .
3. (66) Use partial fractions to find the power series of the function
3
.
(x + 2)(x − 1)
4. (92) Find the sum of the series
∞
X
n
3n
n=1 by calculating f 0 (1/3), where f (x) =
an infinite sum.) P∞ n=0 xn . (Your answer needs to be a number, not 5. (118) Find T2 (x) (the quadratic Taylor polynomial) for the function f (x) = cos(2x)
centered at π.
6. (142) Find the Taylor series for sin x centered at π.
7. (214) Find the Maclaurin series of
Z
F (x) =
0 by integrating ∞ x sin t
dt
t sin t X (−1)n 2n
=
t
t
(2n
+
1)!
n=0
term by term. Additional Problems
6.1 Power Series and Functions 5, 2, 15, 19, 25
6.2 Properties of Power Series 64, 70, 80, 102
6.3 Taylor and Maclaurin Series 130, 146, 154, 158
6.4 Working with Taylor Series 203, 209, 220, 235 Page 2

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Status NEW Posted 10 Jul 2017 12:07 AM My Price 10.00

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