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Exercise 44: Analyzing Limits from the Graph of $y = f(x)$

In this exercise, we are asked to estimate or determine the value of various limits based on the graph provided (Figure 1.18).

Limits:

• $\lim_{x \to 0^-} f(x)$ (a): This is the left-hand limit as $x$ approaches 0. From the graph, the function appears to approach a vertical asymptote, and the value of $f(x)$ tends to $-\infty$.

• $\lim_{x \to 0^+} f(x)$ (b): This is the right-hand limit as $x \to 0$. The graph shows that as $x$ approaches 0 from the right, $f(x)$ tends to $+\infty$.

• $\lim_{x \to 0} f(x)$ (c): Since the left-hand limit tends to $-\infty$ and the right-hand limit tends to ( +\in