**Title: Evaluating Limits and Function Values****Description:**For the function $ h $ whose graph is given below, state the value of each quantity if it exists. If an answer does not exist, enter DNE.**Graph:**The provided graph displays the function $ h(x) $ which fluctuates over the domain from $[-4,7]$. The graph crosses the y-axis, reaches peaks, and valleys, and exhibits different behaviors at different intervals.**Evaluation:**(a) $\lim\limits_{x \to 4} h(x)$ - **Answer:** $\checkmark$ (b) $\lim\limits_{x \to -3^-} h(x)$ - **Answer:** 4 $\checkmark$ (c) $\lim\limits_{x \to -3^+} h(x)$ - **Answer:** DNE (d) $ h(-3) $ - **Answer:** 3 $\redcross$ (e) $\lim\limits_{x \to 0^-} h(x)$ - **Answer:** 1 $\checkmark$(f) $\lim\limits_{x \to 0^+} h(x)$ - **Answer:** -1 $\checkmark$(g) $\lim\limits_{x \to 0} h(x)$ - **Answer:** DNE $\redcross$(h) $ h(0) $ - **Answer:** 0 $\redcross$ (i) $\lim\limits_{x \to 2} h(x)$ - **Answer:** DNE(j) $ h(2) $ - **Answer:** 2 $\redcross$(k) $\lim\limits_{x \to 5^-} h(x)$ - **Answer:** ? $l) \(\lim\limits_{x \to 5^+} h(x)$ - **Answer:** ?(m) $\lim\limits_{x \to 5} h(x)$ - **Answer:** ?Please note that the graph provided indicates variations in the function $ h(x) $ with notable points at $ x=-3, 0, 2, $ and \( 5\

Answered: Image /qna-images/answer/a9446fa9-1d1d-4696-8e49-add0d8a802ea.jpg

Answered: 2- -2 (a) lim h(x) 4 (b) lim x--3* h(x)…

2- -2 (a) lim h(x) 4 (b) lim x--3* h(x) 4 (c) lim h(x) x--3 (d) -3 h(-3) (e) lim h(x) x-0 (f) lim h(x) X-0* -1 lim h(x) TO (g) (h) h(0) (1) lim h(x) x- 2 () h(2) (k) lim h(x) x-5" (1) lim h(x)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.7: A Library Of Parent Functions

Problem 47E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

**Title: Evaluating Limits and Function Values**

**Description:**
For the function $ h $ whose graph is given below, state the value of each quantity if it exists. If an answer does not exist, enter DNE.

**Graph:**
The provided graph displays the function $ h(x) $ which fluctuates over the domain from $[-4,7]$. The graph crosses the y-axis, reaches peaks, and valleys, and exhibits different behaviors at different intervals.

**Evaluation:**

(a) $\lim\limits_{x \to 4} h(x)$
- **Answer:** $\checkmark$

(b) $\lim\limits_{x \to -3^-} h(x)$
- **Answer:** 4 $\checkmark$

(c) $\lim\limits_{x \to -3^+} h(x)$
- **Answer:** DNE

(d) $ h(-3) $
- **Answer:** 3 $\redcross$

(e) $\lim\limits_{x \to 0^-} h(x)$
- **Answer:** 1 $\checkmark$

(f) $\lim\limits_{x \to 0^+} h(x)$
- **Answer:** -1 $\checkmark$

(g) $\lim\limits_{x \to 0} h(x)$
- **Answer:** DNE $\redcross$

(h) $ h(0) $
- **Answer:** 0 $\redcross$

(i) $\lim\limits_{x \to 2} h(x)$
- **Answer:** DNE

(j) $ h(2) $
- **Answer:** 2 $\redcross$

(k) $\lim\limits_{x \to 5^-} h(x)$
- **Answer:** ? \

(l) $\lim\limits_{x \to 5^+} h(x)$
- **Answer:** ?

(m) $\lim\limits_{x \to 5} h(x)$
- **Answer:** ?

Please note that the graph provided indicates variations in the function $ h(x) $ with notable points at $ x=-3, 0, 2, $ and \( 5\

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