Maclaurin series

Calculus

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) =
8
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) =
8

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) = e-2x
f(x) =
8
n = 0
Find the associated radius of convergence R.
R =

4. 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) = ln x, a = 5
f(x) = ln 5 +
8

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) =
8

n = 0
Find the associated radius of convergence R.
R =

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