What is the linear approximation of #g(x)=sqrt(1+x)^(1/5)# at a =0?
(I suppose that you mean x=0)
The function, using the power properties, becomes:
To make a linear approximation of this function it is useful to remember the MacLaurin series, that is the Taylor's polinomial centered in zero.
This series, interrupted to the second power, is:
so the linear approximation of this function is: