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DETAILS SCALC9 1.6.017.
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Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
\[
\lim _{x \rightarrow-4} \frac{x^{2}-2 x-24}{6 x^{2}+23 x-4}
\]
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Answer
Final Answer: The limit of the function as x approaches -4 is \(\boxed{\frac{2}{5}}\).
Step 1 ：The question is asking to find the limit of the function as x approaches -4. The function is a rational function, which is a ratio of two polynomials. The limit of a rational function as x approaches a certain value can be found by substituting that value into the function, if the function is defined at that point. If the function is not defined at that point, we may need to simplify the function or use other limit properties to find the limit.
Step 2 ：Substitute x = -4 into the function: \(f = \frac{x^{2} - 2x - 24}{6x^{2} + 23x - 4}\)
Step 3 ：The limit of the function as x approaches -4 is \(\frac{2}{5}\). This means that as x gets closer and closer to -4, the value of the function gets closer and closer to \(\frac{2}{5}\).
Step 4 ：Final Answer: The limit of the function as x approaches -4 is \(\boxed{\frac{2}{5}}\).
