Question

How do you find the limit of `(tan2x)/(5x)` as x approaches 0?

Answer 1

`lim_{x->0}tan(2x)/(5x) = 2/5`

Explanation:

`tan(2x)/(5x)=sin(2x)/(5x cos(2x)) = ((sin(2x))/(2x))(2/(5 cos(2x)))`

so

`lim_{x->0}tan(2x)/(5x) = lim_{x->0} ((sin(2x))/(2x)) xx lim_{x->0}(2/(5 cos(2x)))`

Finally

`lim_{x->0}tan(2x)/(5x) = 1 xx 2/5 = 2/5`