What is limit x equal to 3, sqrt ( x^2 - 9)/(x - 3).

The limit has
to be determined. If x is substituted with 3, the result is of the form 0/0 which is not
defined.

l'Hospital's rule can be used to find the limit.
For this replace the numerator and denominator by their
derivatives.

This gives
((1/2)*2x*(1/sqrt(x^2 - 9)))/1

=
(x*(1/sqrt(x^2 - 9)))/1

Now substitute x = 3, we get 3/0,
this is equal to infinity as the result of dividing any number by 0 gives
infinity.