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2. For the function f(x) defined by the graph below, with each mark representing one unit, evaluate the following expressions, approximating if necessary: ® (a)_lim_ƒ(x) = . (b) lim f(x) = (c) lim f(x) = (d) lim f(x) = (e) f(1) = (f) Is the function continuous on the domain? Explain.

2. For the function f(x) defined by the graph below, with each mark representing one unit, evaluate the following expressions, approximating if necessary: ® (a)_lim_ƒ(x) = . (b) lim f(x) = (c) lim f(x) = (d) lim f(x) = (e) f(1) = (f) Is the function continuous on the domain? Explain.

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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**Exercise 2:** For the function \( f(x) \) defined by the graph below, with each mark representing one unit, evaluate the following expressions, approximating if necessary: - Graph Description: - The graph shows a piecewise function with points marked on a coordinate grid. - Notable features include a removable discontinuity (open circle) at \( x = 1 \) and a few other distinct points plotted. (a) \(\lim_{{x \to 1^-}} f(x) =\) ____ (b) \(\lim_{{x \to 1^+}} f(x) =\) ____ (c) \(\lim_{{x \to 1}} f(x) =\) ____ (d) \(\lim_{{x \to 5^-}} f(x) =\) ____ (e) \(f(1) =\) ____ (f) Is the function continuous on the domain? Explain. --- **Exercise 3:** For the function \( g \) whose graph is given, state the following: - Graph Description: - The graph depicts a function \( g(x) \) on a coordinate grid. - It includes various curves with both horizontal and vertical segments and a potential vertical asymptote near \( x = -3 \). (a) \(\lim_{{x \to \infty}} g(x) =\) ____ (b) \(\lim_{{x \to 2^+}} g(x) =\) ____ (c) \(\lim_{{x \to -\infty}} g(x) =\) ____ (d) \(\lim_{{x \to 2^-}} g(x) =\) ____ (e) \(\lim_{{x \to -3}} g(x) =\) ____ (f) The equations of the asymptotes, if any. --- This information is useful for students learning about limits and continuity in functions. The graphical approach aids in visual understanding of these key calculus concepts.
Transcribed Image Text:**Exercise 2:** For the function \( f(x) \) defined by the graph below, with each mark representing one unit, evaluate the following expressions, approximating if necessary: - Graph Description: - The graph shows a piecewise function with points marked on a coordinate grid. - Notable features include a removable discontinuity (open circle) at \( x = 1 \) and a few other distinct points plotted. (a) \(\lim_{{x \to 1^-}} f(x) =\) ____ (b) \(\lim_{{x \to 1^+}} f(x) =\) ____ (c) \(\lim_{{x \to 1}} f(x) =\) ____ (d) \(\lim_{{x \to 5^-}} f(x) =\) ____ (e) \(f(1) =\) ____ (f) Is the function continuous on the domain? Explain. --- **Exercise 3:** For the function \( g \) whose graph is given, state the following: - Graph Description: - The graph depicts a function \( g(x) \) on a coordinate grid. - It includes various curves with both horizontal and vertical segments and a potential vertical asymptote near \( x = -3 \). (a) \(\lim_{{x \to \infty}} g(x) =\) ____ (b) \(\lim_{{x \to 2^+}} g(x) =\) ____ (c) \(\lim_{{x \to -\infty}} g(x) =\) ____ (d) \(\lim_{{x \to 2^-}} g(x) =\) ____ (e) \(\lim_{{x \to -3}} g(x) =\) ____ (f) The equations of the asymptotes, if any. --- This information is useful for students learning about limits and continuity in functions. The graphical approach aids in visual understanding of these key calculus concepts.
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