Question

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

Answer #1

find the taylor series of ln 2x centered at x=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) = 2x − 4x3, a = −2

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

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)

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) =xsin(3x) centered at a=π/3 and
Find the radius of convergence of the series you found

Find a Taylor series centered at c for f(x) = ln(x^2), c=1

Find the taylor series for f(x) = ln (1-x) centered at x = 0,
along with the radius and interval of convergance?

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 =?

Find a complete summation formula for the Taylor series
representation of the function f(x) = ln(2x + 3) centered around a
= 1. Hint: you can set the 1st term outside of the summation to not
have to unclude it in the summation formula.

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