Question

lim x--> 3 (3 - x)/ (x^2 - 9)

I know the answer is -1/6, but I can't figure out how to get there.

Answer 1

Le'Hoptial's Rule is a good application here, but I suspect you have not had that yet.

That rule states that if you have an indeterminate form of a limit, such as 0/0, then that limit is the same as the limit of the derivative of the numerator /derivative of denominator.

Here , you have the form 0/0, so take the derivativ of the numerator (-1) and divide it by the derivative of the denominator (2x). Now let x>>3