Let f(x) = \sin(5x). Find the 6th Taylor polynomial.

amolent3u

amolent3u

Answered question

2021-12-08

Let f(x)=sin(5x). Find the 6th Taylor polynomial.

Answer & Explanation

Bertha Jordan

Bertha Jordan

Beginner2021-12-09Added 37 answers

Step 1 Given function:
f(x)=sin5x
The Taylor series expansion of sin x is given by:
sinx=x13!x3+15!x517!x7+
Step 2
Now,
sinx=x13!x3+15!x517!x7+
Now,
Replace x by 5x:
sin5x=5x13!(5x)3+15!(5x)517!(5x)7+
=5x1256x3+62524x5156251008x7+
Therefore,
T6(x)=5x1256x3+62524x5156251008x7+

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