Question

What is the limit as x approaches 0 of `tan(x)/sin(x)`?

Answer 1

`lim_(x->0)tanx/sinx=1`

Explanation:

Plugging in `0` right away yields `tan(0)/sin(0)=0/0,` an indeterminate form, so we must simplify.

Recall `tanx=sinx/cosx.`

So,

`lim_(x->0)tanx/sinx=lim_(x->0)(sinx/cosx)/sinx=lim_(x->0)cancelsinx/(cosxcancelsinx)=lim_(x->0)secx=sec0=1`