Question

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

Answer 1

The limit does not exist.

Explanation:

As `xrarr-3`, the numerator is negative.

the denominator is negative or positive and goes to `0` (depending on whether `x` goes to `-3` from the left or from the right.

`lim_(xrarr-3^-) x/(x+3) = (-3)/(0^-) = oo`

`lim_(xrarr-3^+) x/(x+3) = (-3)/(0^+) = - oo`

`lim_(xrarr-3) x/(x+3)` `" "` Does Not Exist