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) = sin(x), a = pi/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) = 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) = 2x − 4x3, a = −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) = 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 R n ( x ) → 0 . f ( x ) = ln x , a = 5
f(x)=∞∑n =?

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

Known f (x) = sin (2x)
a. Find the Taylor series expansion around x = pi / 2, up to 5
terms only.
b. Determine Maclaurin's series expansion, up to 4 terms only

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

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.

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

Find the power series expansion for f(x) = x^2 e^(x^2) centered
at a = 0 and centered at a=-3

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