Taylor polynomials Find the nth-order Taylor polynomial for the following

Lennie Davis

Lennie Davis

Answered question

2021-12-17

Taylor polynomials Find the nth-order Taylor polynomial for the following functions centered at the given point a.
f(x)=sin2x,n=3,a=0

Answer & Explanation

abonirali59

abonirali59

Beginner2021-12-18Added 35 answers

Step 1
Given function is f(x)=sin2x and n = 3, a = 0.
Series can be written as follows.
p3(x)=f(0)+f(0)(x0)+f(0)2!(x0)2+f(0)3!(x0)3.
Step 2
Compute the derivatives value at a=0.
f(x)=sin2xf(0)=0
f(x)=2cos2xf(0)=2
f(x)=4sin2xf(0)=0
f(x)=8cos2xf(0)=8
Obtain the Taylor polynomial.
p3(x)=f(0)+f(0)(x0)+f(0)2!(x0)2+f(0)3!(x0)3
=0+2x+08x33!
=2x4x33

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