Question

How do you find the linear approximation to `f(x) = ln (1-x)` at x =0?

Answer 1

`f(x) ~= -x` around `x=0`

Explanation:

You can use the MacLaurin development of `f(x)` and stop at the first order:

`f(x) = f(0) +f'(0)x + o(x^2)`

so:

`f(x) ~= ln(1-0) -(1/(1-0)) x =-x`