Question

for the function f whose graph is given, determine the limits in parts a. through l. below. write ∞ or -∞ where appropriate. a. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim f(x)=□ (x→4) b. the limit does not exist and is neither -∞ nor ∞.

Explanation:

Step1: Analyze left - hand limit

As $x$ approaches $4$ from the left side ($x\to4^{-}$), observe the $y -$ values of the function on the graph.

Step2: Analyze right - hand limit

As $x$ approaches $4$ from the right side ($x\to4^{+}$), observe the $y -$ values of the function on the graph.

Step3: Compare left - hand and right - hand limits

If $\lim_{x\to4^{-}}f(x)=\lim_{x\to4^{+}}f(x)=L$, then $\lim_{x\to4}f(x) = L$. If they are not equal, the limit does not exist. From the graph, as $x$ approaches $4$ from the left, the function values go to $-\infty$, and as $x$ approaches $4$ from the right, the function values go to $\infty$. Since the left - hand limit and right - hand limit are not equal, the limit does not exist and is neither $-\infty$ nor $\infty$.

Answer:

B. The limit does not exist and is neither $-\infty$ nor $\infty$.