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X 13 -2 lim f(x)= x-14 lim f(x)= x-14 lim f(x)=\ x-14+ aluate the following limits: 13.9 -2 13.99 -2 14 -8 14.01 -2 14.1 15 -2 -2

X 13 -2 lim f(x)= x-14 lim f(x)= x-14 lim f(x)=\ x-14+ aluate the following limits: 13.9 -2 13.99 -2 14 -8 14.01 -2 14.1 15 -2 -2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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### Evaluating Limits Using Tables #### Question 1 Use the table to evaluate the following limits: | \( x \) | 13 | 13.9 | 13.99 | 14 | 14.01 | 14.1 | 15 | |-----------|-----|------|-------|-------|-------|------|-----| | \( f(x) \) | -2 | -2 | -2 | -8 | -2 | -2 | -2 | Evaluate the limits: - \( \lim_{{x \to 14}} f(x) = \) - \( \lim_{{x \to 14^-}} f(x) = \) - \( \lim_{{x \to 14^+}} f(x) = \) Click "Submit" when finished. --- #### Question 3 Use the table to evaluate the following limits: | \( x \) | 11 | 11.9 | 11.99 | 12 | 12.01 | 12.1 | 13 | |-----------|------|------|-------|------|-------|------|-----| | \( f(x) \) | -39 | -42.6| -42.96| 16 | 16.01 | 16.1 | 17 | Evaluate the limits: - \( \lim_{{x \to 12}} f(x) = \) - \( \lim_{{x \to 12^-}} f(x) = \) - \( \lim_{{x \to 12^+}} f(x) = \) Click "Submit" when finished. --- ### Explanation These tables provide values for \( f(x) \) at various points around the target values. You can use these values to determine the behavior of \( f(x) \) as \( x \) approaches the specified limits. Notice the difference between approaching a limit from the left (\( 14^- \) or \( 12^- \)) and from the right (\( 14^+ \) or \( 12^+ \)).
Transcribed Image Text:### Evaluating Limits Using Tables #### Question 1 Use the table to evaluate the following limits: | \( x \) | 13 | 13.9 | 13.99 | 14 | 14.01 | 14.1 | 15 | |-----------|-----|------|-------|-------|-------|------|-----| | \( f(x) \) | -2 | -2 | -2 | -8 | -2 | -2 | -2 | Evaluate the limits: - \( \lim_{{x \to 14}} f(x) = \) - \( \lim_{{x \to 14^-}} f(x) = \) - \( \lim_{{x \to 14^+}} f(x) = \) Click "Submit" when finished. --- #### Question 3 Use the table to evaluate the following limits: | \( x \) | 11 | 11.9 | 11.99 | 12 | 12.01 | 12.1 | 13 | |-----------|------|------|-------|------|-------|------|-----| | \( f(x) \) | -39 | -42.6| -42.96| 16 | 16.01 | 16.1 | 17 | Evaluate the limits: - \( \lim_{{x \to 12}} f(x) = \) - \( \lim_{{x \to 12^-}} f(x) = \) - \( \lim_{{x \to 12^+}} f(x) = \) Click "Submit" when finished. --- ### Explanation These tables provide values for \( f(x) \) at various points around the target values. You can use these values to determine the behavior of \( f(x) \) as \( x \) approaches the specified limits. Notice the difference between approaching a limit from the left (\( 14^- \) or \( 12^- \)) and from the right (\( 14^+ \) or \( 12^+ \)).
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