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**Educational Content on Limits** **Topic: Evaluating Limits Using a Table** Consider the limit of \( f(x) \) as \( x \) approaches 4, where \( f(x) = \frac{x^2 - 16}{x - 4} \). **A. Find the limit below if they exist by completing the following input-output table.** **a.** \(\lim_{{x \to 4^-}} f(x)\) | \(x \to 4^-\) | \(f(x)\) | |---------------|----------| | 3.9999 | | | 3.99 | | | 3.9 | | **b.** \(\lim_{{x \to 4^+}} f(x)\) | \(x \to 4^+\) | \(f(x)\) | |---------------|----------| | 4.0001 | | | 4.001 | | | 4.01 | | **B. Find \(\lim_{{x \to 4}}\) of \(f(x)\) algebraically. Show all work.** --- This content provides a structured approach to evaluating limits numerically by using tables to ascertain the behavior of \( f(x) \) as \( x \) approaches 4 from both the left and right. It also requires an algebraic solution to confirm the limit analytically.

**Educational Content on Limits** **Topic: Evaluating Limits Using a Table** Consider the limit of \( f(x) \) as \( x \) approaches 4, where \( f(x) = \frac{x^2 - 16}{x - 4} \). **A. Find the limit below if they exist by completing the following input-output table.** **a.** \(\lim_{{x \to 4^-}} f(x)\) | \(x \to 4^-\) | \(f(x)\) | |---------------|----------| | 3.9999 | | | 3.99 | | | 3.9 | | **b.** \(\lim_{{x \to 4^+}} f(x)\) | \(x \to 4^+\) | \(f(x)\) | |---------------|----------| | 4.0001 | | | 4.001 | | | 4.01 | | **B. Find \(\lim_{{x \to 4}}\) of \(f(x)\) algebraically. Show all work.** --- This content provides a structured approach to evaluating limits numerically by using tables to ascertain the behavior of \( f(x) \) as \( x \) approaches 4 from both the left and right. It also requires an algebraic solution to confirm the limit analytically.

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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**Educational Content on Limits** **Topic: Evaluating Limits Using a Table** Consider the limit of \( f(x) \) as \( x \) approaches 4, where \( f(x) = \frac{x^2 - 16}{x - 4} \). **A. Find the limit below if they exist by completing the following input-output table.** **a.** \(\lim_{{x \to 4^-}} f(x)\) | \(x \to 4^-\) | \(f(x)\) | |---------------|----------| | 3.9999 | | | 3.99 | | | 3.9 | | **b.** \(\lim_{{x \to 4^+}} f(x)\) | \(x \to 4^+\) | \(f(x)\) | |---------------|----------| | 4.0001 | | | 4.001 | | | 4.01 | | **B. Find \(\lim_{{x \to 4}}\) of \(f(x)\) algebraically. Show all work.** --- This content provides a structured approach to evaluating limits numerically by using tables to ascertain the behavior of \( f(x) \) as \( x \) approaches 4 from both the left and right. It also requires an algebraic solution to confirm the limit analytically.
Transcribed Image Text:**Educational Content on Limits** **Topic: Evaluating Limits Using a Table** Consider the limit of \( f(x) \) as \( x \) approaches 4, where \( f(x) = \frac{x^2 - 16}{x - 4} \). **A. Find the limit below if they exist by completing the following input-output table.** **a.** \(\lim_{{x \to 4^-}} f(x)\) | \(x \to 4^-\) | \(f(x)\) | |---------------|----------| | 3.9999 | | | 3.99 | | | 3.9 | | **b.** \(\lim_{{x \to 4^+}} f(x)\) | \(x \to 4^+\) | \(f(x)\) | |---------------|----------| | 4.0001 | | | 4.001 | | | 4.01 | | **B. Find \(\lim_{{x \to 4}}\) of \(f(x)\) algebraically. Show all work.** --- This content provides a structured approach to evaluating limits numerically by using tables to ascertain the behavior of \( f(x) \) as \( x \) approaches 4 from both the left and right. It also requires an algebraic solution to confirm the limit analytically.
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