Question

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

Answer #1

1) find the Taylor series expansion of
f(x)=ln(x) center at 2 first then find its associated radius of
convergence.
2) Find the radius of convergence and interval
of convergence of the series Σ (x^n)/(2n-1) upper infinity lower
n=1

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 =

Find the power series representation for the function: f(x) =
x2 / (1+2x)2 Determine the radius of
convergence.

Find a power series representation for the function.
f(x)=x^3/(x-8)^2
f(x)=SIGMA n=0 to infinity
Determine the radius of convergence
Use a Maclaurin series in this table to obtain the Maclaurin
series for the given function
f(x)=xcos(2x)

Find a power series representation for f(x) = ln(x^7 + 2), and
find its radius of convergence.

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

Find a power series expansion for the function f(x)=1/x wither
center a=-3. What is its radius of convergence?

The hyperbolic cosine function, cosh x = (1/2) (e^x + e^-x).
Find the Taylor series representation for cosh x centered at x=0 by
using the well known Taylor series expansion of e^x. What is the
radius of convergence of the Taylor Expansion?

Problem 15:
Find the taylor series for f (x) = cos (2x) around x = pi/4, and
find its interval and radius of convergence.

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

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 12 minutes ago

asked 17 minutes ago

asked 19 minutes ago

asked 20 minutes ago

asked 30 minutes ago

asked 30 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago