Question

Find the Taylor series for the function using the definition of Taylor series.

f(x) = cos2x , a = pi

Answer #1

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

Use the definition of Taylor series to find the Taylor series
(centered at c) for the function.
f (x) = e3x, c = 0

Find the Taylor series for the function f(x)=sin(pi(x)-pi/2)
with center a=1

Find the Taylor Series at a=pi/2 for f(x)=5cos(x).

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

Use the definition of Taylor series to find the first five terms
of f(x)=lnx centered at a=2. simplify all coefficients

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
Rn(x) → 0.]
f(x) = sin(x), a = pi/2

Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x) centered at
the given value of a. (Enter your answers as a
comma-separated list.)
f(x) = 4/(1+x), a = 2
Use the definition of a Taylor series to find the first four
nonzero terms of the series for f(x) centered at
the given value of a. (Enter your answers as a
comma-separated list.)
f(x) = 3xe^x, a = 0

For this problem, consider the function f(x) = ln(1 + x).
(a) Write the Taylor series expansion for f(x) based at b = 0. Give
your
final answer in Σ notation using one sigma sign. (You may use 4
basic Taylor
series in TN4 to find the Taylor series for f(x).)
(b) Find f(2020) (0).
Please answer both questions, cause it will be hard to post them
separately.

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