Find the linear approximation of the function.

Question

g(x) = ^3sqrt(1 + x) at a = 0.

g(x)≈

Use to approximate these numbers (round to 3rd decimal)
3^sqrt(.95)

3^sqrt(1.1)

Answer 1

g'(x) = 1/3 (1+x)^(-2/3)
g'(0) = 1/3
g(0) = 1
so the linear approximation is g(x) ≈ 1 + 1/3 x