Question

Suppose the power series for a function f(x) has the interval of convergence I=(a,b]. Which of the following statement must be true about the interval of convergence for the power series \int f(x)dx?

I=[a,b)

I=(a,b)

I=(a,b]

I=[a,b]

Can't be determined.

Answer #1

Find a power series representation for the function; determine
the interval of convergence. f(X) = (3x^2)/(5x+1)

Find the interval of convergence of the power
series f ( x ) = ∑ n = 1 ∞ ( x + 3 ) n 2 n.

Find a power series representation for the function; find the
interval of convergence. (Give your power series representation
centered at x = 0.) f(x) = (x2 + 1)/ (2x − 1)

Evaluate integral 1/1+x^9 dx as a power series. Give the
interval of convergence of the power series.

Problem 7
Find a power series representation for the function and
determine the interval of convergence.
f(x)=(2x+3)/(x2+3x+2)

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...

1. Use a power series to approximate the definite integral, I,
to six decimal places. 0.4 to 0, (x5 / 1 + x6 ) dx
2. Find a power series representation for the function. (Give
your power series representation centered at x = 0.)
f(x) = ln(9 − x). Determine the radius of convergence, R. I
already found the first part to be x is 1/n(x/9)^n but can't find
R

Find a power series representation for the function. (Give your
power series representation centered at x = 0.)
f(x) =
8
3 −
x
f(x) =
∞
n = 0
Determine the interval of convergence. (Enter your answer using
interval notation.)

Find a power series representation for the function and
determine the radius of convergence.
1) f(x)=x^3/(x-2)^2
2) f(x)=arctan(x/3)

Find a power series representation for the function. (Give your
power series representation centered at x = 0.)
f(x) = (x^2) / (x^4 +16 )
Determine the interval of convergence. (Enter your answer using
interval notation.)

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 45 seconds ago

asked 12 minutes ago

asked 20 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago