Question

**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

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

Find the 4th degree, T4 taylor polynomial for f(x)=arctan (x)
centered at c=1/2 and use it to aproximate f(x)= arctan
(1/16)

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

Find the second degree polynomial of Taylor series for f(x)=
1/(lnx)^3 centered at c=2. Write step by step.

For the function f(x) = ln(4x), find the 3rd order Taylor
Polynomial 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) = e^x, a = ln(2)

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 of f(x)=x^2 * arctan(x^2) at b = 0

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