Question

Find the coefficient of the fourth term, that is, the coefficient of (x-a)^4 of the Taylor series around x=a for the function (x)= xe^(2x)

a) e^(2a)(a+1)/15

b) e^(2a)(4a+6)/3

c) e^(2a)(2a+4)/3

d) e^(2a)(4a+10)/15

e) other answer

Answer #1

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

1.)Find T5(x), the degree 5 Taylor polynomial of the function
f(x)=cos(x) at a=0.
T5(x)=
Find all values of x for which this approximation is within
0.003452 of the right answer. Assume for simplicity that we limit
ourselves to |x|≤1.
|x|≤
2.) (1 point) Use substitution to find the Taylor series of
(e^(−5x)) at the point a=0. Your answers should not include the
variable x. Finally, determine the general term an in
(e^(−5x))=∑n=0∞ (an(x^n))
e^(−5x)= + x + x^2
+ x^3 + ... = ∑∞n=0...

Find a complete summation formula for the Taylor series
representation of the function f(x) = ln(2x + 3) centered around a
= 1. Hint: you can set the 1st term outside of the summation to not
have to unclude it in the summation formula.

1. Consider the function f(x) = 2x^2 - 7x + 9
a) Find the second-degree Taylor series for f(x) centered at x =
0. Show all work.
b) Find the second-degree Taylor series for f(x) centered at x =
1. Write it as a power series centered around x = 1, and then
distribute all terms. What do you notice?

1. Find T5(x): Taylor polynomial of degree 5 of the function
f(x)=cos(x) at a=0.
T5(x)=
Using the Taylor Remainder Theorem, find all values of x
for which this approximation is within 0.00054 of the right answer.
Assume for simplicity that we limit ourselves to |x|≤1.
|x|≤ =
2. Use the appropriate substitutions to write down the first
four nonzero terms of the Maclaurin series for the binomial:
(1+7x)^1/4
The first nonzero term is:
The second nonzero term is:
The third...

Find the Taylor series for f(x) = e^3+2x centered at x = −1.

Known f (x) = sin (2x)
a. Find the Taylor series expansion around x = pi / 2, up to 5
terms only.
b. Determine Maclaurin's series expansion, up to 4 terms only

Find the general term for the Taylor series for xarctan(x/3)

For f(x) = 3 + 7x − 19x^2 + 2x^4, use complete Horner’s
algorithm to find
(a) the Maclaurin series (Taylor series about x = 0)
(b) the Taylor series for this function about x = 2.

Find the Taylor Series of the given function centered at the
indicated point.
x^4 at a = -1
so x^4=

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