Question

How do you evaluate the limit `x^3/(tan^3(2x)` as x approaches `0`?

Answer 1

See below

Explanation:

`x^3/tan^3(2x) = x^3/(sin^2(2x)/cos^3(2x))`

`= (x/sin(2x))^3 * cos^3(2x)`

`= 1/8((2x)/sin(2x))^3 * cos^3(2x)`

Limit as `xrarr0` is

`1/8 * (1)^3 * (1)^3 = 1/8`