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Use the table to evaluate the following limits: x f(x) lim f(x)= -9 lim f(x)= 2-9+ lim f(x) = 2-9 8 8.9 -27 -30.6 8.99 9 -30.96 13 9.01 13.01 9.1 10 13.1 14

Use the table to evaluate the following limits: x f(x) lim f(x)= -9 lim f(x)= 2-9+ lim f(x) = 2-9 8 8.9 -27 -30.6 8.99 9 -30.96 13 9.01 13.01 9.1 10 13.1 14

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.6: Absolute Value Functions
Problem 32SE: Use a graphing utility to graph f(x)=10|x-|2 on the viewing window [0,4] . Identify the...
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### Evaluating Limits Using a Table In this exercise, we will utilize a table to evaluate specific limits as \( x \) approaches 9. The table provides the values of \( f(x) \) for specific values of \( x \): | \( x \) | 8 | 8.9 | 8.99 | 9 | 9.01 | 9.1 | 10 | |--------|----|------|-------|----|------|------|-----| | \( f(x) \) | -27 | -30.6 | -30.96 | 13 | 13.01 | 13.1 | 14 | Based on this table, evaluate the following limits: 1. \( \lim_{{x \to 9^-}} f(x) = \) 2. \( \lim_{{x \to 9^+}} f(x) = \) 3. \( \lim_{{x \to 9}} f(x) = \) ### Explanation of the Table: #### Table Details: - The table consists of two rows. - The first row shows the values of \( x \): 8, 8.9, 8.99, 9, 9.01, 9.1, and 10. - The second row shows the corresponding values of \( f(x) \): -27, -30.6, -30.96, 13, 13.01, 13.1, and 14. #### Graph/Diagram Explanation: - The table is a representation of the function \( f(x) \) around the point \( x = 9 \). - As \( x \) approaches 9 from the left (\( x \to 9^- \)), the values of \( f(x) \) are -27, -30.6, and -30.96. - As \( x \) approaches 9 from the right (\( x \to 9^+ \)), the values of \( f(x) \) are 13, 13.01, and 13.1. Given this data: - **\(\lim_{{x \to 9^-}} f(x)\)** evaluates the limit of \( f(x) \) as \( x \) approaches 9 from the left. - **\(\lim_{{x
Transcribed Image Text:### Evaluating Limits Using a Table In this exercise, we will utilize a table to evaluate specific limits as \( x \) approaches 9. The table provides the values of \( f(x) \) for specific values of \( x \): | \( x \) | 8 | 8.9 | 8.99 | 9 | 9.01 | 9.1 | 10 | |--------|----|------|-------|----|------|------|-----| | \( f(x) \) | -27 | -30.6 | -30.96 | 13 | 13.01 | 13.1 | 14 | Based on this table, evaluate the following limits: 1. \( \lim_{{x \to 9^-}} f(x) = \) 2. \( \lim_{{x \to 9^+}} f(x) = \) 3. \( \lim_{{x \to 9}} f(x) = \) ### Explanation of the Table: #### Table Details: - The table consists of two rows. - The first row shows the values of \( x \): 8, 8.9, 8.99, 9, 9.01, 9.1, and 10. - The second row shows the corresponding values of \( f(x) \): -27, -30.6, -30.96, 13, 13.01, 13.1, and 14. #### Graph/Diagram Explanation: - The table is a representation of the function \( f(x) \) around the point \( x = 9 \). - As \( x \) approaches 9 from the left (\( x \to 9^- \)), the values of \( f(x) \) are -27, -30.6, and -30.96. - As \( x \) approaches 9 from the right (\( x \to 9^+ \)), the values of \( f(x) \) are 13, 13.01, and 13.1. Given this data: - **\(\lim_{{x \to 9^-}} f(x)\)** evaluates the limit of \( f(x) \) as \( x \) approaches 9 from the left. - **\(\lim_{{x
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