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 Rn(x) → 0.] f(x) = e^x, a = ln(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) = 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) = 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 =?

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

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

PART A: Find the Taylor series for ln x
centered at x = 5
PART B: Find the second degree Taylor
polynomial for f (x) = arctan x centered at x = 0

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

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

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

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