Question

How do you find the limit of `tanx` as `x->pi`?

Answer 1

`lim_(x->pi) tan(x)=0`

Explanation:

This limit can be evaluated by simply substituting in `pi` since `tan` is continuous and defined at `pi`:

`lim_(x->pi) tan(x)=tan(pi)`

In case we have forgotten the value of `tan(pi)`, we can use the following identity to figure it out:
`tan(theta)=sin(theta)/cos(theta)`

This gives:
`tan(pi)=sin(pi)/cos(pi)=0/(-1)=0`