Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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**Transcription for Educational Website:** --- ### Use the graph to find the following limits and function value. **a.** \(\lim_{{x \to 2^-}} f(x)\) **b.** \(\lim_{{x \to 2^+}} f(x)\) **c.** \(\lim_{{x \to 2}} f(x)\) **d.** \(f(2)\) --- ### Graph Explanation The graph provided is a depiction of a function \( f(x) \) on a coordinate plane, with the x-axis and y-axis labeled. - The function appears to change direction at various points, showing a curve passing through different y-values as x-values increase. - At \( x = 2 \), there is an open circle on the curve which indicates a discontinuity or that the function is not defined at that exact point for \( f(x) \). - The curve approaches this open circle from both the left (\( x \to 2^- \)) and right (\( x \to 2^+ \)) sides, which are relevant for evaluating one-sided limits. - There is a filled point at a higher y-value directly above \( x = 2 \), indicating that \( f(2) \) takes this y-value. - The graph also shows other peaks and troughs around these points, hinting at the oscillatory nature of \( f(x) \). The limits and function value sought in the questions involve examining the behavior of the graph around \( x = 2 \).
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Transcribed Image Text:**Transcription for Educational Website:** --- ### Use the graph to find the following limits and function value. **a.** \(\lim_{{x \to 2^-}} f(x)\) **b.** \(\lim_{{x \to 2^+}} f(x)\) **c.** \(\lim_{{x \to 2}} f(x)\) **d.** \(f(2)\) --- ### Graph Explanation The graph provided is a depiction of a function \( f(x) \) on a coordinate plane, with the x-axis and y-axis labeled. - The function appears to change direction at various points, showing a curve passing through different y-values as x-values increase. - At \( x = 2 \), there is an open circle on the curve which indicates a discontinuity or that the function is not defined at that exact point for \( f(x) \). - The curve approaches this open circle from both the left (\( x \to 2^- \)) and right (\( x \to 2^+ \)) sides, which are relevant for evaluating one-sided limits. - There is a filled point at a higher y-value directly above \( x = 2 \), indicating that \( f(2) \) takes this y-value. - The graph also shows other peaks and troughs around these points, hinting at the oscillatory nature of \( f(x) \). The limits and function value sought in the questions involve examining the behavior of the graph around \( x = 2 \).
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