Let f(x)=\cos(2x)+7. Compute the following Taylor polynomials of f. For any approximations, you should use around 6 decimals.

e1s2kat26

e1s2kat26

Answered question

2021-09-03

Let f(x)=cos(2x)+7. Compute the following Taylor polynomials of f. For any approximations, you should use around 6 decimals.

Answer & Explanation

opsadnojD

opsadnojD

Skilled2021-09-04Added 95 answers

From the given problem:
f(x)=cos(2x)+7
Let centered at a=0
From the Taylor series:
f(x)=f(a)+f(a)1!(xa)+f(a)2!(xa)2+f(a)3!(xa)3+ (1)
So,
f(x)=d(cos(2x)+7)dx=ddx(cos(2x))+ddx(7)=2sin(2x)
f=d(2sin(2x))dx=cos(2x)ddx(2x)=4cos(2x)
f(x)=d(4cos(2x))dx=sin(2x)ddx(2x)=8sin(2x)
f4(x)=d(8sin(2x))dx=cos(2x)ddx(2x)=16cos(2x)
At a=0
f(0)=cos(2×0)+7=8
f(0)=2sin(2×0)=0
f(0)=4cos(2×0)=4
f(0)=8sin(2×0)=0
f4(0)=16cos(2×0)=16
Now substitute these values in equation (1).

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?