Questions: Use the Theorem on Limits of Rational Functions to find the limit. If necessary, state that the limit does not exist. lim (x -> -8) (x^2 - 6) / (8 - x) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. lim (x -> -8) (x^2 - 6) / (8 - x) = (Simplify your answer.) B. The limit does not exist.

Use the Theorem on Limits of Rational Functions to find the limit. If necessary, state that the limit does not exist.

lim (x -> -8) (x^2 - 6) / (8 - x)

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
lim (x -> -8) (x^2 - 6) / (8 - x) = (Simplify your answer.)
B. The limit does not exist.
Transcript text: Use the Theorem on Limits of Rational Functions to find the limit. If necessary, state that the limit does not exist. \[ \lim _{x \rightarrow-8} \frac{x^{2}-6}{8-x} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $\lim _{x \rightarrow-8} \frac{x^{2}-6}{8-x}=$ $\square$ (Simplify your answer.) B. The limit does not exist.
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Solution

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Solution Steps

Step 1: Identify the function and the point of interest

The function given is \(f(x) = (x^2-6)/(8-x)\) and we are interested in the limit as \(x\) approaches -8.

Step 2: Check if direct substitution is possible

Direct substitution of \(x = -8\) into \(f(x)\) gives \(f(-8) = 29/8\), which is not indeterminate.

Step 3: Apply limit laws or simplify if necessary

No further simplification was necessary.

Final Answer:

The limit of \(f(x)\) as \(x\) approaches -8 is 3.625.

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