Question

What is lim x→-3 sqrt x^2-8

Answer 1

If the  -8 is under the square root, then...

$\displaystyle L = \lim_{x\to -3} \sqrt{x^2-8}\\\\L = \sqrt{(-3)^2-8}\\\\L = \sqrt{9-8}\\\\L = \sqrt{1}\\\\L = 1$

OR

If the -8 is not under the square root, then...

$\displaystyle L = \lim_{x\to -3} \sqrt{x^2}-8\\\\L = \sqrt{(-3)^2}-8\\\\L = \sqrt{9}-8\\\\L = 3-8\\\\L = -5$

Either way, we replace x with -3 and simplify.

For more information, refer to the direct substitution rule for limits.