Question

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

Answer #1

We are given

we can use taylor series formula

now, we can find values

now, we can plug values

and we get

we can simplify it

**............Answer**

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

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

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 =?

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 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.

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

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