Use the linear approximation (1+x) ^kapprox 1+kx to find an approximation for the function f (x) for values of x near zero.

a.) f (x) = (1-x) ^ (8) approx

b.) f (x) = - 8 / (1-x) = approx

c.) f (x) = 1 / (sqrt (1+x)) = approx

d.) f (x) = sqrt (4+x^2) approx =

e.) f (x) = (6+3x) ^ (1/3) approx =

Question

Mathematics

Adams

18 February, 21:18

Use the linear approximation (1+x) ^kapprox 1+kx to find an approximation for the function f (x) for values of x near zero.

a.) f (x) = (1-x) ^ (8) approx

b.) f (x) = - 8 / (1-x) = approx

c.) f (x) = 1 / (sqrt (1+x)) = approx

d.) f (x) = sqrt (4+x^2) approx =

e.) f (x) = (6+3x) ^ (1/3) approx =

+2

Answers (1)

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Grease · Answer 1

A) approx = 1-8x

b) f (x) - 8 (1-x) ^-1 approx = - 8 (1+x) = - 8 - 8x

because 1/x = x^-1 ...

c) f (x) = (1+x) ^-1/2 approx = 1 - 1/2x

d) f (x) = (4+x^2) ^1/2 approx = 4 + 1/2x^2

e) f (x) = (6+3x) ^1/3 approx = 6+x

Use the linear approximation (1+x) ^kapprox 1+kx to find an approximation for the function f (x) for values of x near zero.a.) f (x) = (1-x) ^ (8) approxb.) f (x) = - 8 / (1-x) = approxc.) f (x) = 1 / (sqrt (1+x)) = approxd.) f (x) = sqrt (4+x^2) approx =e.) f (x) = (6+3x) ^ (1/3) approx =