Question

How do you determine the limit of `3/(x+1)` as x approaches -1?

Answer 1

`lim_"x-> -1" 3/(x+1)` does not exist

Explanation:

First consider `lim_"x->-1" 3/(x+1)` from `x<-1` This limit `-> -oo`

Then consider `lim_"x->-1" 3/(x+1)` from `x> -1` This limit `-> +oo`

Hence the limit diverges.

This can be easily be seen from the graph of `3/(x+1)` in the region of `x=-1` below:

graph{3/(x+1) [-12.66, 12.64, -6.32, 6.34]}