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**Graph Analysis and Limit Evaluation** Use the given graph of \( f \) to state the value of each quantity if it exists. (If an answer does not exist, enter DNE.) ### Graph Explanation The graph provided depicts a function \( f(x) \) with the x-axis ranging from 0 to 5 and the y-axis ranging from 0 to 5. The curve shows different behaviors at key points: - There is a discontinuity where \( x = 2 \). - The function appears to approach different values from the left and right at \( x = 2 \). - The curve is continuous at \( x = 4 \). ### Questions: (a) \(\lim_{{x \to 2^-}} f(x)\) (b) \(\lim_{{x \to 2^+}} f(x)\) (c) \(\lim_{{x \to 2}} f(x)\) (d) \( f(2) \) (e) \(\lim_{{x \to 4}} f(x)\) (f) \( f(4) \) ### Answers: (d) \( f(2) \): DNE (e) \(\lim_{{x \to 4}} f(x)\): The limit of \( f(x) \) as \( x \) approaches 4. The function is continuous at this point, so we take the value 2. (f) \( f(4) \): DNE

**Graph Analysis and Limit Evaluation** Use the given graph of \( f \) to state the value of each quantity if it exists. (If an answer does not exist, enter DNE.) ### Graph Explanation The graph provided depicts a function \( f(x) \) with the x-axis ranging from 0 to 5 and the y-axis ranging from 0 to 5. The curve shows different behaviors at key points: - There is a discontinuity where \( x = 2 \). - The function appears to approach different values from the left and right at \( x = 2 \). - The curve is continuous at \( x = 4 \). ### Questions: (a) \(\lim_{{x \to 2^-}} f(x)\) (b) \(\lim_{{x \to 2^+}} f(x)\) (c) \(\lim_{{x \to 2}} f(x)\) (d) \( f(2) \) (e) \(\lim_{{x \to 4}} f(x)\) (f) \( f(4) \) ### Answers: (d) \( f(2) \): DNE (e) \(\lim_{{x \to 4}} f(x)\): The limit of \( f(x) \) as \( x \) approaches 4. The function is continuous at this point, so we take the value 2. (f) \( f(4) \): DNE

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 Analysis and Limit Evaluation** Use the given graph of \( f \) to state the value of each quantity if it exists. (If an answer does not exist, enter DNE.) ### Graph Explanation The graph provided depicts a function \( f(x) \) with the x-axis ranging from 0 to 5 and the y-axis ranging from 0 to 5. The curve shows different behaviors at key points: - There is a discontinuity where \( x = 2 \). - The function appears to approach different values from the left and right at \( x = 2 \). - The curve is continuous at \( x = 4 \). ### Questions: (a) \(\lim_{{x \to 2^-}} f(x)\) (b) \(\lim_{{x \to 2^+}} f(x)\) (c) \(\lim_{{x \to 2}} f(x)\) (d) \( f(2) \) (e) \(\lim_{{x \to 4}} f(x)\) (f) \( f(4) \) ### Answers: (d) \( f(2) \): DNE (e) \(\lim_{{x \to 4}} f(x)\): The limit of \( f(x) \) as \( x \) approaches 4. The function is continuous at this point, so we take the value 2. (f) \( f(4) \): DNE
Transcribed Image Text:**Graph Analysis and Limit Evaluation** Use the given graph of \( f \) to state the value of each quantity if it exists. (If an answer does not exist, enter DNE.) ### Graph Explanation The graph provided depicts a function \( f(x) \) with the x-axis ranging from 0 to 5 and the y-axis ranging from 0 to 5. The curve shows different behaviors at key points: - There is a discontinuity where \( x = 2 \). - The function appears to approach different values from the left and right at \( x = 2 \). - The curve is continuous at \( x = 4 \). ### Questions: (a) \(\lim_{{x \to 2^-}} f(x)\) (b) \(\lim_{{x \to 2^+}} f(x)\) (c) \(\lim_{{x \to 2}} f(x)\) (d) \( f(2) \) (e) \(\lim_{{x \to 4}} f(x)\) (f) \( f(4) \) ### Answers: (d) \( f(2) \): DNE (e) \(\lim_{{x \to 4}} f(x)\): The limit of \( f(x) \) as \( x \) approaches 4. The function is continuous at this point, so we take the value 2. (f) \( f(4) \): DNE
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