# Project #77305 - Calculus II Problems

1. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that

Rn(x 0.]

f(x) = 3(1  x)2

(x) =
 ∞ n = 0

Find the associated radius of convergence R.
R =

2. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x 0.]
f(x) = ln(1 + 2x)
f(x) =
 ∞ n = 1

Find the associated radius of convergence R.
R =

3. Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that
Rn(x 0.]
f(x) = e2x
f(x) =
 ∞ n = 0

Find the associated radius of convergence R.
R =

4. Find the Taylor series for f(xcentered at the given value of a. [Assume that f has a power series expansion. Do not show that

Rn(x 0.

]

f(x) = ln x,  a = 5
f(x) = ln 5 +
 ∞ n = 1

Find the associated radius of convergence R.
R =

5. 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 Rn(x 0.]

f(x) =
 2 x
,   a = 4
f(x) =
 ∞ n = 0

Find the associated radius of convergence R.
R =

 Subject Mathematics Due By (Pacific Time) 07/24/2015 06:00 pm
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