limit quesiton need help

Question

I need help on a relatively simple limit equation. If possible, evaluate:

lim (4(8−𝑥))/(𝑥^2 2−64)

𝑥→8

Answer 1

Hi, Tanaka:

I'm assuming that "𝑥^2 2" in the denominator is a typo and should be just x^2.

Then, lim 4(8 - x)/(x² - 64) is of indeterminate form 0/0 at x = 8. Therefore, we can use L'Hopital's rule

𝑥→8

= lim (-4 / 2x) which is not indeterminate at x =8, so we can plug that value in.

𝑥→8

= -4/16

= -1/4