-2 (a) lim h(x) X--3 (b) lim h(x) x--3+ lim h(x) x- -3 (d) h(-3) (e) lim h(x) X- 0 1 lim h(x) x- 0+ (f) -1 lim h(x) X -0 (g) -1 (h) h(0) 1 (i) lim h(x) X- 2 one G) h(2)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Topic: Limits and Function Values**

For the function \( h \) whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)

**Graph Explanation:**
The graph depicts a continuous function \( h(x) \) over the domain from \( x = -5 \) to \( x = 8 \). The vertical axis is labeled \( y \), ranging from \( -2 \) to 4. Note that between \( x = 5 \) to \( x = 6 \), the function oscillates rapidly, indicating possible non-existence of limits within this interval.

**Limit and Function Value Analysis:**

(a) \( \lim_{x \to -3} h(x) \)
   **Answer:** 4 ✓

(b) \( \lim_{x \to -3^+} h(x) \)
   **Answer:** 4 ✓

(c) \( \lim_{x \to -3^-} h(x) \)
   **Answer:** 0 ✗

(d) \( h(-3) \)
   **Answer:** 0 ✗

(e) \( \lim_{x \to 0^-} h(x) \)
   **Answer:** 1 ✓

(f) \( \lim_{x \to 0^+} h(x) \)
   **Answer:** -1 ✓

(g) \( \lim_{x \to 0} h(x) \)
   **Answer:** -1 ✗

(h) \( h(0) \)
   **Answer:** 1 ✓

(i) \( \lim_{x \to 2} h(x) \)
   **Answer:** one ✗

(j) \( h(2) \)
   **Answer:** DNE ✓

(k) \( \lim_{x \to 5^-} h(x) \)
   **Answer:** 3 ✓

(l) \( \lim_{x \to 5^+} h(x) \)
   **Answer:** 3 ✗

For further assistance, click on the "Need Help?" or "Read It" buttons provided at the bottom of the page.
Transcribed Image Text:**Topic: Limits and Function Values** For the function \( h \) whose graph is given, state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.) **Graph Explanation:** The graph depicts a continuous function \( h(x) \) over the domain from \( x = -5 \) to \( x = 8 \). The vertical axis is labeled \( y \), ranging from \( -2 \) to 4. Note that between \( x = 5 \) to \( x = 6 \), the function oscillates rapidly, indicating possible non-existence of limits within this interval. **Limit and Function Value Analysis:** (a) \( \lim_{x \to -3} h(x) \) **Answer:** 4 ✓ (b) \( \lim_{x \to -3^+} h(x) \) **Answer:** 4 ✓ (c) \( \lim_{x \to -3^-} h(x) \) **Answer:** 0 ✗ (d) \( h(-3) \) **Answer:** 0 ✗ (e) \( \lim_{x \to 0^-} h(x) \) **Answer:** 1 ✓ (f) \( \lim_{x \to 0^+} h(x) \) **Answer:** -1 ✓ (g) \( \lim_{x \to 0} h(x) \) **Answer:** -1 ✗ (h) \( h(0) \) **Answer:** 1 ✓ (i) \( \lim_{x \to 2} h(x) \) **Answer:** one ✗ (j) \( h(2) \) **Answer:** DNE ✓ (k) \( \lim_{x \to 5^-} h(x) \) **Answer:** 3 ✓ (l) \( \lim_{x \to 5^+} h(x) \) **Answer:** 3 ✗ For further assistance, click on the "Need Help?" or "Read It" buttons provided at the bottom of the page.
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