Question

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

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.

Find the Taylor series for the function f(x)=sin(pi(x)-pi/2)
with center a=1

sin(x)=x-x3/3!+x5/5!
Below is the expansion of the Taylor series sin (x) function around the x = [x] point.
Please continue.

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) = sin(x), a = pi/2

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

Find the Taylor Series at a=pi/2 for f(x)=5cos(x).

Find the Taylor series for f(x)= sinx at a=pi/6. (Find up to the
fifth degree)

Find the 5th Taylor polynomial of f(x) = 1 + x + 2x^5
+sin(x^2) based at b = 0.

How to find the first three terms of the Maclaurin Series for
f(x) = sin(2*pi*x).

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?

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