Question

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
*R*_{n}(*x*) → 0.]

f(x) = 2x − 4x^{3}, a = −2

Answer #1

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) = e^x, a = ln(2)

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) = sin(x), a = pi/2

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) = xcos(x), a = pi

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 R n ( x ) → 0 . f ( x ) = ln x , a = 5
f(x)=∞∑n =?

1. Consider the function f(x) = 2x^2 - 7x + 9
a) Find the second-degree Taylor series for f(x) centered at x =
0. Show all work.
b) Find the second-degree Taylor series for f(x) centered at x =
1. Write it as a power series centered around x = 1, and then
distribute all terms. What do you notice?

Find the Taylor series for f(x) = e^3+2x centered at x = −1.

Use
the definition of a Taylor Series to find the taylor series for
f(x) = e^(-x/2) centered at 0

A) Find the first 4 nonzero terms of the Taylor series for the
given function centered at a = pi/2
B) Write the power series using summation notation
f(x) = sinx

find the taylor series of ln 2x centered at x=2

Consider the Taylor Series for f(x) = 1/ x^2 centered at x =
-1
a.) Express this Taylor Series as a Power Series using summation
notation.
b.) Determine the interval of convergence for this Taylor
Series.

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