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Use the graph below to find the indicated limits. If a limit doesn't exist, state doesn't exist, state undefined. -3 VA 0. 2 5 11 val X

Use the graph below to find the indicated limits. If a limit doesn't exist, state doesn't exist, state undefined. -3 VA 0. 2 5 11 val X

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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**Limits and Continuity Worksheet** **Objective:** Use the graph below to find the indicated limits. If a limit doesn’t exist, state DNE. If value doesn’t exist, state undefined. ### Graph Explanation The graph shows a function \( f(x) \) plotted on a coordinate plane. The x-axis ranges approximately from -4 to 7, while the y-axis ranges approximately from -10 to 10. The function has a piecewise character, with distinct behaviors in the different intervals: - For \( x < -3 \), the function seems to increase as x approaches \(-3\). - Just before \( x = -3 \), the function appears to reach a high value, and then drops suddenly. - As \( x \) progresses towards 0, the function rises again, reaches a peak at \( x = 0 \), and then declines. - Beyond \( x = 0 \) and approaching \( x = 2 \), the function reaches a minimum. - From \( x = 2 \) onwards, the function rises sharply again, and continues increasing beyond \( x = 5 \). Given this detailed behavior, use the relevant sections of the graph to determine the limits as specified in the exercises. ### Exercises (n) \(\lim_{{x \to 6^+}} f(x)\) For this specific exercise: - As \( x \) approaches 6 from the right, observe the behavior of \( f(x) \). - Using the graph, determine whether \( f(x) \) approaches a specific value, increases indefinitely, decreases indefinitely, or oscillates without approaching a specific value. **Answer Key:** Ensure to write down DNE if the limit does not exist at \( x \rightarrow 6^+ \), and Undefined if the value itself is undefined. Remember, understanding the patterns and behaviors around the critical points on the graph is essential for accurate limit determination. Happy solving!
Transcribed Image Text:**Limits and Continuity Worksheet** **Objective:** Use the graph below to find the indicated limits. If a limit doesn’t exist, state DNE. If value doesn’t exist, state undefined. ### Graph Explanation The graph shows a function \( f(x) \) plotted on a coordinate plane. The x-axis ranges approximately from -4 to 7, while the y-axis ranges approximately from -10 to 10. The function has a piecewise character, with distinct behaviors in the different intervals: - For \( x < -3 \), the function seems to increase as x approaches \(-3\). - Just before \( x = -3 \), the function appears to reach a high value, and then drops suddenly. - As \( x \) progresses towards 0, the function rises again, reaches a peak at \( x = 0 \), and then declines. - Beyond \( x = 0 \) and approaching \( x = 2 \), the function reaches a minimum. - From \( x = 2 \) onwards, the function rises sharply again, and continues increasing beyond \( x = 5 \). Given this detailed behavior, use the relevant sections of the graph to determine the limits as specified in the exercises. ### Exercises (n) \(\lim_{{x \to 6^+}} f(x)\) For this specific exercise: - As \( x \) approaches 6 from the right, observe the behavior of \( f(x) \). - Using the graph, determine whether \( f(x) \) approaches a specific value, increases indefinitely, decreases indefinitely, or oscillates without approaching a specific value. **Answer Key:** Ensure to write down DNE if the limit does not exist at \( x \rightarrow 6^+ \), and Undefined if the value itself is undefined. Remember, understanding the patterns and behaviors around the critical points on the graph is essential for accurate limit determination. Happy solving!
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