Question

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?

Answer #1

(1 point) Find the degree 3 Taylor polynomial T3(x) centered
at a=4 of the function f(x)=(7x−20)4/3.
T3(x)=
? True False Cannot be determined The function f(x)=(7x−20)4/3
equals its third degree Taylor polynomial T3(x) centered at a=4.
Hint: Graph both of them. If it looks like they are equal, then do
the algebra.

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 second degree polynomial of Taylor series for f(x)=
1/(lnx)^3 centered at c=2. Write step by step.

Find the Taylor series for f(x) centered at
the given value of a. [Assume that f has a power
series expansion. Do not show that
Rn(x) → 0.]
f(x) = 2x − 4x3, a = −2

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 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.

Find the degree 3 Taylor polynomial T3(x) of function
f(x)=(7x−5)^3/2 at a=2. T3(x)=

(1 point) Find the degree 3 Taylor polynomial T3(x) of
function
f(x)=(7x+67)^(5/4)
at a=2
T3(x)=?

Find the degree 3 Taylor polynomial T3 (x) centered
at a = 4 of the function f(x) = (-7x+36)4/3

1-(Partial Fraction Decomposition Revisited) Consider the
rational function 1/(1-x)(1-2x)
(a) Find power series expansions separately for 1/(1 − x) and
1/(1 − 2x).
(b) Multiply these two power series expansions together to get a
power series ex-pansion for
1 (1−x)(1−2x)
(This involves doing an infinite amount of distributing and
combining coeffi-cients, but you should be able to figure out the
pattern here.)
c) Separate the power series in terms of power series for A/(1 −
x) and B/(1 − 2x)...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 12 minutes ago

asked 12 minutes ago

asked 48 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago