If , then and . So we have an indeterminate form, , use l'H˘pital's rule.
The answer is 15.
A standard way to find limits of the form where is to multiply the numerator and the denominator by to get
where the latter expression does not have a singularity at .
For this problem, use the same idea and the fact that
Equivalently, factor out 5 and represent x - 2 in the numerator as (x - 1) - 1 and then factor it according to (*).