question on finfind limits!?

Question

how do you find the limits of this? the answer IS -1/2..but I have no idea how you approach that answer..if would be great..if you worked out theproblem

lim rad(x^2 - 9)/2x-6
x => infiniti

Answer 1

I'd say that the function of which you're trying to find the limit is the square root of (x^2-9)/(2x-6)^2. The limit of the square root is just the square root of the limit. The limit of (x^2 + lower order terms)/((4x^2+lower order terms) is 1/4. The square root of 1/4 is 1/2.

I have no idea where you got the minus sign from in your proposed answer.

To make this more formal, L'Hopital's Rule would help.

Or as an alternate to my method, you could try to apply L'Hopital's Rule right from the start (i.e., to the original quotient given in the problem).