Approximating powers Compute the coefficients for the Taylor series for the following functions about the given point a, and then use the first four terms of the series to approximate the given number. f(x)=frac{1}{sqrt{x}} with a=4, approximate frac{1}{sqrt{3}}

Falak Kinney

Falak Kinney

Answered question

2021-02-05

Approximating powers Compute the coefficients for the Taylor series for the following functions about the given point a, and then use the first four terms of the series to approximate the given number.
f(x)=1x with a=4, approximate 13

Answer & Explanation

Clelioo

Clelioo

Skilled2021-02-06Added 88 answers

Consider the provided function,
f(x)=1x with a=4, approximate 13
Compute the coefficients for the Taylor series for the following functions about the given point a, and then use the first four terms of the series to approximate the given number.
The Taylor series as a form of k=0ck(xa)k, where ck=fk(a)k!,k=0,1,2,
We evaluate the derivative of the function at point a=4
f(x)=1xf(4)=12
f(x)=12x32f(4)=116
f(x)=34x52f(4)=3128
f(x)=158x72f(4)=151024
Hence, the first four term of the series is shown below.
12116(x4)+3128(x4)2151024(x4)3
So,13=12116(134)+3128(134)2151024(134)3
=12143163+4932412835(1452043)10243
=12+166832731024
Hence.

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