Use the linear approximation (1+x)^{k}\approx 1+kx to find an approximation

aidmoong7

aidmoong7

Answered question

2021-12-06

Use the linear approximation (1+x)k1+kx to find an approximation for the function f(x) for values of x near zero.
f(x)=3{(1x2+x)2}

Answer & Explanation

mylouscrapza

mylouscrapza

Beginner2021-12-07Added 22 answers

Use the linear approximation (1+x)k1+kx to find an approximation for the following functions for values of x near zero.
f(x)=3{(1x2+x)2}=(1x2+x)23=[1+(x2+x)]23
1+23(x2+x)=12x3(2+x)=12x6+3x=6+3x2x6+3x=6+x6+3x
Result:
f(x)6+x6+3x

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