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j(x) 3 -6 -1 16. Use the graph above to evaluate j(x) for the following (a) What is the lim j(x) = (b) What is the lim j(r) = (c) What is the lim j(x) = 2-3

j(x) 3 -6 -1 16. Use the graph above to evaluate j(x) for the following (a) What is the lim j(x) = (b) What is the lim j(r) = (c) What is the lim j(x) = 2-3

Calculus: Early Transcendentals
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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### Graph Description and Questions The image depicts a graph of the function \( j(x) \) plotted on a coordinate grid. Key features include: - **Axes:** The horizontal axis is marked as \( x \) and the vertical axis is marked as \( j(x) \). - **Points:** The graph has various open and closed circles indicating specific values of \( j(x) \). ### Key Graph Points: - At \( x = -4 \), the graph has an open circle at \( j(x) = -1 \). - At \( x = -3 \), there is a closed circle at \( j(x) = 0 \). - At \( x = 0 \), the graph shows a peak with a closed circle at \( j(x) = 4 \). - At \( x = 2 \), there are open circles around \( j(x) = -3 \). - As \( x \) approaches positive or negative infinity, the graph seems to tend towards a linear path. ### Questions: 16. Use the graph above to evaluate \( j(x) \) for the following (a) What is the \(\lim_{x \to 4} j(x) =\) (b) What is the \(\lim_{x \to 2} j(x) = \) (c) What is the \(\lim_{x \to -3} j(x) = \) (d) What is the \(\lim_{x \to -2} j(x) = \) (e) What is the \(\lim_{x \to 0} j(x) = \) (f) Circle on the graph all places where \( j'(x) = 0 \) (g) Where is \( j(x) \) non-differentiable? ### Explanation of Graph Features: - **Curves and Slopes:** The graph's slope changes at various points, indicating transitions in the derivative \( j'(x) \). - **Non-Differentiable Points:** These are likely at sharp corners, endpoints with open circles, or where the graph is not smooth. - **Derivative Zeros (Critical Points):** Found at local maxima or minima, where \( j(x) \) does not increase or decrease. Reviewing these, students are tasked with evaluating limits, identifying points of non-differentiability, and marking where the derivative equals zero. These exercises enhance understanding of continuity and differentiability in calculus
Transcribed Image Text:### Graph Description and Questions The image depicts a graph of the function \( j(x) \) plotted on a coordinate grid. Key features include: - **Axes:** The horizontal axis is marked as \( x \) and the vertical axis is marked as \( j(x) \). - **Points:** The graph has various open and closed circles indicating specific values of \( j(x) \). ### Key Graph Points: - At \( x = -4 \), the graph has an open circle at \( j(x) = -1 \). - At \( x = -3 \), there is a closed circle at \( j(x) = 0 \). - At \( x = 0 \), the graph shows a peak with a closed circle at \( j(x) = 4 \). - At \( x = 2 \), there are open circles around \( j(x) = -3 \). - As \( x \) approaches positive or negative infinity, the graph seems to tend towards a linear path. ### Questions: 16. Use the graph above to evaluate \( j(x) \) for the following (a) What is the \(\lim_{x \to 4} j(x) =\) (b) What is the \(\lim_{x \to 2} j(x) = \) (c) What is the \(\lim_{x \to -3} j(x) = \) (d) What is the \(\lim_{x \to -2} j(x) = \) (e) What is the \(\lim_{x \to 0} j(x) = \) (f) Circle on the graph all places where \( j'(x) = 0 \) (g) Where is \( j(x) \) non-differentiable? ### Explanation of Graph Features: - **Curves and Slopes:** The graph's slope changes at various points, indicating transitions in the derivative \( j'(x) \). - **Non-Differentiable Points:** These are likely at sharp corners, endpoints with open circles, or where the graph is not smooth. - **Derivative Zeros (Critical Points):** Found at local maxima or minima, where \( j(x) \) does not increase or decrease. Reviewing these, students are tasked with evaluating limits, identifying points of non-differentiability, and marking where the derivative equals zero. These exercises enhance understanding of continuity and differentiability in calculus
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