Question

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

Answer #1

Use a power series to approximate the definite integral to 4
decimal places: from 0 to 1/2 (x^2)(e^(-x^2) dx. Find power series
of e^-x^2. and the value of the integral (how many terms
needed)

Find a power series representation for the function.
f(x) = ln(5 − x)
f(x) = ln(5) +
∞
(−1)nn(x5)n
n = 0
Determine the radius of convergence, R.
R =

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...

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

Use power series to approximate 1/(1+x^10) then calculate
integral .

1. Evaluate the definite integral given
below.
∫(from 0 to π/3) (2sin(x)+3cos(x)) dx
2. Given F(x) below, find F′(x).
F(x)=∫(from 2 to ln(x)) (t^2+9)dt
3. Evaluate the definite integral given
below.
∫(from 0 to 2) (−5x^3/4 + 2x^1/4)dx

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 radius of convergence, R, of the series. ∞ n = 1 (x +
6)n / 6n ln(n)
and find the interval of convergence

let
f(x)=ln(1+2x)
a. find the taylor series expansion of f(x) with center at
x=0
b. determine the radius of convergence of this power
series
c. discuss if it is appropriate to use power series
representation of f(x) to predict the valuesof f(x) at x= 0.1, 0.9,
1.5. justify your answe

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 15 minutes ago

asked 16 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 19 minutes ago

asked 19 minutes ago

asked 24 minutes ago

asked 28 minutes ago

asked 38 minutes ago

asked 43 minutes ago

asked 50 minutes ago