Question

How do you find the linearization at a=1 of `f(x) = 2 ln(x)`?

Answer 1

`L(x)=2(x-1)`

Explanation:

`f(x)=2ln x Rightarrow f(1)=2ln(1)=0`

`f'(x)=2/x Rightarrow f'(1)=2/1=2`

Linearization `L(x)` of `f` at `a=1` is:

`L(x)=f(a)+f'(a)(x-a)=f(1)+f'(1)(x-1)=2(x-1)`

I hope that this was clear.