Question

find the limit, if it exists.
lim(x→9⁻) √(x² - 81)
9√3
0
4.5
does not exist

Explanation:

Step1: Analyze the function near $x = 9^-$

When $x\to9^-$, we consider values of $x$ that are less than 9 but approaching 9. For the function $y = \sqrt{x^{2}-81}$, when $x<9$, say $x = 9 - h$ where $h>0$ and $h\to0$. Then $x^{2}-81=(9 - h)^{2}-81=81-18h+h^{2}-81=h^{2}-18h=h(h - 18)$. As $x\to9^-$, $x^{2}-81<0$. Since the square - root of a negative number is not a real number in the set of real numbers.

Answer:

Does not exist