Questions: Use the given graph of the function y=f(x) to find the following quantities, if they exist. (If an answer does not exist, enter DNE.) (a) lim x -> 2 f(x) (b) lim x -> 5- f(x) (c) lim x -> 5+ f(x)

Use the given graph of the function y=f(x) to find the following quantities, if they exist. (If an answer does not exist, enter DNE.)
(a) lim x -> 2 f(x)
(b) lim x -> 5- f(x)
(c) lim x -> 5+ f(x)

Transcript text: Use the given graph of the function $y=f(x)$ to find the following quantities, if they exist. (If an answer does not exist, enter DNE.) (a) $\lim _{x \rightarrow 2} f(x)$ (b) $\lim _{x \rightarrow 5^{-}} f(x)$ (c) $\lim _{x \rightarrow 5^{+}} f(x)$

Solution

Solution Steps

Step 1: Find the limit as x approaches 2.

The graph of f(x) is continuous around x = 2. As x approaches 2 from both the left and the right, f(x) approaches 3. Therefore, $\lim_{x \rightarrow 2} f(x) = 3$.

Step 2: Find the limit as x approaches 5 from the left.

As x approaches 5 from the left, f(x) approaches 4. Therefore, $\lim_{x \rightarrow 5^{-}} f(x) = 4$.

Step 3: Find the limit as x approaches 5 from the right.

As x approaches 5 from the right, f(x) approaches 2. Therefore, $\lim_{x \rightarrow 5^{+}} f(x) = 2$.