Questions: Homework: HW 2 Question Completed: 2 of 23 Part 5 of 5 My score: 1.75 / 23 pts (7.61%) Use the graph of h in the given figure to find the following values or state that they do not exist. (a) h(5) (b) lim x -> 5 h(x) (c) h(7) (d) lim x -> 7 h(x) (e) lim x -> 8 h(x) A. lim x -> 7 h(x)=4 (Type an integer or a decimal.) B. The limit does not exist. (e) Find lim x -> 8 h(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. lim x -> 8 h(x)= (Type an integer or a decimal.) B. The limit does not exist.

Homework: HW 2 Question Completed: 2 of 23 Part 5 of 5 My score: 1.75 / 23 pts (7.61%) Use the graph of h in the given figure to find the following values or state that they do not exist. (a) h(5) (b) lim x -> 5 h(x) (c) h(7) (d) lim x -> 7 h(x) (e) lim x -> 8 h(x) A. lim x -> 7 h(x)=4 (Type an integer or a decimal.) B. The limit does not exist. (e) Find lim x -> 8 h(x). Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. lim x -> 8 h(x)= (Type an integer or a decimal.) B. The limit does not exist.
Transcript text: Homework: HW 2 Question Completed: 2 of 23 Part 5 of $5 \quad$ My score: $1.75 / 23$ pts (7.61\%) Use the graph of h in the given figure to find the following values or state that they do not exist. (a) $h(5)$ (b) $\lim _{x \rightarrow 5} h(x)$ (c) $h(7)$ (d) $\lim _{x \rightarrow 7} h(x)$ (e) $\lim _{x \rightarrow 8} h(x)$ A. $\lim _{x \rightarrow 7} h(x)=4$ (Type an integer or a decimal.) B. The limit does not exist. (e) Find $\lim _{x \rightarrow 8} h(x)$. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. $\lim _{x \rightarrow 8} h(x)=\square$ (Type an integer or a decimal.) B. The limit does not exist.
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Solution

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Solution Steps

Step 1: Find h(5)

The value of h(5) is the y-value of the function h at x = 5. Looking at the graph, we see an open circle at (5, 6) and a filled circle at (5, 8). The filled circle represents the value of the function. Therefore, h(5) = 8.

Step 2: Find the limit as x approaches 5

The limit of h(x) as x approaches 5 is the y-value that the function approaches as x gets closer to 5 from both the left and the right. As x approaches 5 from the left, h(x) approaches 6. As x approaches 5 from the right, h(x) approaches 6. Since the function approaches the same value from both sides, the limit exists and is equal to 6.

Step 3: Find h(7)

The value of h(7) is the y-value of the function h at x = 7. Looking at the graph, we find an open circle at (7, 4). Therefore, h(7) = 4.

Final Answer

\(h(5) = \boxed{8}\) \(\lim_{x \rightarrow 5} h(x) = \boxed{6}\) \(h(7) = \boxed{4}\)

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