Use the graph of h(x) shown below to evaluate limh(x), if possible. If the limit does not exist, enter Ø. 0 trex) Provide your answer below: lim (x)= -4 -2. 4 & 9 9 1
Use the graph of h(x) shown below to evaluate limh(x), if possible. If the limit does not exist, enter Ø. 0 trex) Provide your answer below: lim (x)= -4 -2. 4 & 9 9 1
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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![### Question
Use the graph of \( h(x) \) shown below to evaluate \( \lim_{x \to -6} h(x) \), if possible. If the limit does not exist, enter ∅.
**Graph Analysis:**
The graph of \( h(x) \) is a continuous curve with several peaks and troughs. The x-axis ranges from -12 to 10, and the y-axis ranges from -10 to 6. There is a noticeable behavior at \( x = -6 \):
- The graph approaches different y-values from the left and right of \( x = -6 \).
- As \( x \) approaches -6 from the left, \( h(x) \) approaches approximately 3.
- As \( x \) approaches -6 from the right, \( h(x) \) approaches approximately -8.
- There is a blue dot at the point (-6, -8) indicating the value of the function \( h(-6) = -8 \).
Since the left-hand limit \( \lim_{x \to -6^-} h(x) \) and the right-hand limit \( \lim_{x \to -6^+} h(x) \) are not equal, the overall limit \( \lim_{x \to -6} h(x) \) does not exist.
**Graphical Representation:**
- The graph crosses the y-axis at approximately \( y = 1 \).
- It has a peak at around \( x = -4 \) and a trough at around \( x = 4 \).
- The curve is smooth and appears to be a polynomial function.
**Provide your answer below:**
\[ \lim_{x \to -6} h(x) = \boxed{\varnothing} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffcf92b5-4154-452a-af6b-b4e696e552b0%2F17636597-99da-46e1-9f4c-7366eae740b1%2Feh61pdi_processed.png&w=3840&q=75)
Transcribed Image Text:### Question
Use the graph of \( h(x) \) shown below to evaluate \( \lim_{x \to -6} h(x) \), if possible. If the limit does not exist, enter ∅.
**Graph Analysis:**
The graph of \( h(x) \) is a continuous curve with several peaks and troughs. The x-axis ranges from -12 to 10, and the y-axis ranges from -10 to 6. There is a noticeable behavior at \( x = -6 \):
- The graph approaches different y-values from the left and right of \( x = -6 \).
- As \( x \) approaches -6 from the left, \( h(x) \) approaches approximately 3.
- As \( x \) approaches -6 from the right, \( h(x) \) approaches approximately -8.
- There is a blue dot at the point (-6, -8) indicating the value of the function \( h(-6) = -8 \).
Since the left-hand limit \( \lim_{x \to -6^-} h(x) \) and the right-hand limit \( \lim_{x \to -6^+} h(x) \) are not equal, the overall limit \( \lim_{x \to -6} h(x) \) does not exist.
**Graphical Representation:**
- The graph crosses the y-axis at approximately \( y = 1 \).
- It has a peak at around \( x = -4 \) and a trough at around \( x = 4 \).
- The curve is smooth and appears to be a polynomial function.
**Provide your answer below:**
\[ \lim_{x \to -6} h(x) = \boxed{\varnothing} \]
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