Question

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 =

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