Question

Find the radius and interval of convergence for the taylor series centered at x=0 for g(x)=x^2ln(1+x/3). Please show work.

Answer #1

Comment If any problem.

Find the Taylor series for f(x) =xsin(3x) centered at a=π/3 and
Find the radius of convergence of the series you found

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

1) Find the radius of convergence, R, of the series and Find the
interval of convergence, I, of the series. (Enter your answer using
interval notation.)
∞
4nxn
n2
n = 1
2) Find the radius of convergence, R, of the series.
Find the interval of convergence, I, of the series. (Enter
your answer using interval notation.)
∞
(x −
4)n
n7 + 1
n = 0

Find the taylor series of f(x) = xsin(x4) at x=1 and
determine the radius of convergence.

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.

Find the Taylor series and associated radius of convergence for
?(?) = cos? at ? = ?/3

Find the MacLaurin series for f(x) = cos(5x^3 ) and its radius
of convergence.
Find the degree four Taylor polynomial, T4(x), for g(x) = sin(x)
at a = π/4.

(3)
(a) Why does it not make sense to find the Taylor series of f(x)
= √3 x at a = 0?
(b) Without calculating the Taylor series, explain why the
radius of convergence for the Taylor series of f(x) = 1 (x−3)(x+7)
at a = 0 cannot be more than 3. (You may assume the Taylor series
is equal to the function when it converges.)

Find the radius of convergence, R of the series. And find the
interval of, I, of convergence of the series.
The sum from n=1 to infinity: (4^n)(n^2)(x^n)

1) Find the interval of convergence I of the series.
(Enter your answer using interval notation.)
∞
7n (x +
5)n
n
n = 1
2) Find the radius of convergence, R, of the following
series.
∞
n!(7x
− 1)n
n = 1
3) Suppose that the radius of convergence of the power
series
cn xn
is R.
What is the radius of convergence of the power series
cn x5n
?
4) Find the radius of convergence, R, of the...

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