Question

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

Explanation:

Step1: Analyze the function as $x\to9^{-}$

Let $f(x)=\sqrt{x^{2}-81}$. When $x\to9^{-}$, we consider values of $x$ that are less than 9 but approaching 9. For $x < 9$, $x^{2}-81<0$. Since the square - root of a negative number is not a real number in the set of real numbers.

Step2: Determine the limit

The expression $\sqrt{x^{2}-81}$ has no real - valued limit as $x\to9^{-}$ because the quantity inside the square - root, $x^{2}-81$, is negative for $x\in(0,9)$.

Answer:

C. Does not exist