Question

How do you evaluate the limit `(2tan^2x)/x^2` as x approaches `0`?

Answer 1

`lim_(x->0)2tan^2x/(x^2) = 2`

Explanation:

Considering that:

`tanx=sinx/cosx`

We have that:

`2tan^2x/(x^2) = 2* (sinx/x)^2*1/(cos^2x)`

So:

`lim_(x->0)2tan^2x/(x^2) = lim_(x->0)[2* (sinx/x)^2*1/(cos^2x)] = 2*1^2*1/(1^2) =2`