Question

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

Answer 1

See below.

Explanation:

`(2tan^2x)/x^2 = (2sin^2x)/(x^2cos^2x)`

`= 2*sinx/x * sinx/x * 1/cos^2x`

As `xrarr0`, the above goes to

`2(1)(1)1/(1^2) = 2`