How do you find the limit of x/sqrt(x^2-9)xx29 as x->3^-x3?

1 Answer
Dec 7, 2016

The limit does not exist.

Explanation:

If we are staying in the real numbers, then the domain of the function is (-oo,-3) uu (3,oo)(,3)(3,) so we cannot approach positive 3 from the left.

If we are allowed to use imaginary numbers, then the limit still does not exist, because as x approaches 3 from the left, the numerator goes to 3 and the denominator goes to 00 (through purely imaginary values).