Question

How do you find the limit of `x/sqrt(9-x^2)` as x approaches -3+?

Answer 1

`hlim_(xrarr-3^+) x/sqrt(9-x^2) = -oo` (Does not exist because as xrarr-3^+ , the ratio decreases without bound.)

As `xrarr-3^+`, the numerator approaches `-3` and the denominator approaches `0` through positive values. So the fraction is negative and getting more negative as `xrarr-3`.