Question

the graph of f shown below has vertical asymptotes at \\(x = -3\\) and \\(x = 5\\). analyze the following limits.

a. \\(\lim_{x \to -3^-} f(x)\\)
b. \\(\lim_{x \to -3^+} f(x)\\)
c. \\(\lim_{x \to -3} f(x)\\)
d. \\(\lim_{x \to 5^-} f(x)\\)
e. \\(\lim_{x \to 5^+} f(x)\\)
f. \\(\lim_{x \to 5} f(x)\\)

f. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. \\(\lim_{x \to 5} f(x) = \\)
b. the limit does not exist and is neither \\(\infty\\) nor \\(-\infty\\)

Explanation:

Analyze the one-sided limits at \(x = 5\)

$$
LATEXBLOCK0
$$

Evaluate the two-sided limit at \(x = 5\)

$$ \lim_{x \to 5^-} f(x) e \lim_{x \to 5^+} f(x) \implies \lim_{x \to 5} f(x) \text{ does not exist} $$

Determine the correct multiple-choice option

Since one side goes to \(-\infty\) and the other goes to \(\infty\), the two-sided limit does not exist and is neither \(\infty\) nor \(-\infty\).

Answer:

• A. \(\lim_{x \to 5} f(x) = \)
• B. The limit does not exist and is neither \(\infty\) nor \(-\infty\) (Correct answer)