Questions: Use the graph of the function f shown to estimate the indicated limits and the function value. a. lim x→-1^- f(x) b. lim x→-1^+ f(x) c. lim x→-1 f(x) d. f(-1)

Transcript text: Use the graph of the function $f$ shown to estimate the indicated limits and the function value. a. $\lim _{x \rightarrow-1^{-}} f(x)$ b. $\lim _{x \rightarrow-1^{+}} f(x)$ c. $\lim _{x \rightarrow-1} f(x)$ d. $f(-1)$

Solution

Solution Steps

Step 1: Estimate the limit as x approaches -1 from the right

To find $\lim_{{x \to -1^+}} f(x)$, observe the graph as $x$ approaches -1 from the right. The function value approaches 2.

Step 2: Estimate the limit as x approaches -1 from the left

To find $\lim_{{x \to -1^-}} f(x)$, observe the graph as $x$ approaches -1 from the left. The function value approaches -1.

Step 3: Estimate the limit as x approaches -1

To find $\lim_{{x \to -1}} f(x)$, check if the left-hand limit and right-hand limit are equal. Since $\lim_{{x \to -1^+}} f(x) = 2$ and $\lim_{{x \to -1^-}} f(x) = -1$, the limit does not exist.