Find the linear approximation of the function g(x)=cube root(1+x) at a=0.

Answer 1

Assuming you meant x=0,

g'(x) = 1/3 (1+x)^(-2/3)
g'(0) = 1/3

So, the line going through (0,1) with slope 1/3 is ?

See

http://www.wolframalpha.com/input/?i=plot+y%3D%281%2Bx%29^%281%2F3%29%2C+y%3Dx%2F3%2B1+for+-1%3C%3Dx%3C%3D2