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Evaluate each expression using the graph of g(x) shown, assuming the scale is 1. If a value does not exist, write "DNE." a. g(0) b. g(2) c. lim g(x) d. lim g(x) e. lim g(x) f. lim g(x) X-2 Let f(x) = {x² + 2x - 1, r<2, x-9, x>2 .Evaluate each expression below. If a value does not exist, write "DNE." a. f(2) b. lim f(x) c. lim f(x) 4-x, x<1 Let p(x) = -x+ c, x21 Find the value of c so that lim p(x) exists.

Evaluate each expression using the graph of g(x) shown, assuming the scale is 1. If a value does not exist, write "DNE." a. g(0) b. g(2) c. lim g(x) d. lim g(x) e. lim g(x) f. lim g(x) X-2 Let f(x) = {x² + 2x - 1, r<2, x-9, x>2 .Evaluate each expression below. If a value does not exist, write "DNE." a. f(2) b. lim f(x) c. lim f(x) 4-x, x<1 Let p(x) = -x+ c, x21 Find the value of c so that lim p(x) exists.

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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**Evaluate each expression using the graph of \( g(x) \) shown, assuming the scale is 1. If a value does not exist, write "DNE."** a. \( g(0) \) b. \( g(2) \) c. \(\lim_{{x \to 0}} g(x)\) d. \(\lim_{{x \to 2^-}} g(x)\) e. \(\lim_{{x \to 2^+}} g(x)\) f. \(\lim_{{x \to 2}} g(x)\) The graph provided is a piecewise curve with multiple direction changes and special points, indicating possible local maximums, minimums, and discontinuities. The x-values particularly relevant for this problem include 0 and 2. **Let \( f(x) = \begin{cases} x^2 + 2x - 1, & x < 2 \\ x^3 - 9, & x > 2 \end{cases} \). Evaluate each expression below. If a value does not exist, write "DNE."** a. \( f(2) \) b. \(\lim_{{x \to 2^-}} f(x)\) c. \(\lim_{{x \to 2^+}} f(x)\) **Let \( p(x) = \begin{cases} 4-x, & x < 1 \\ -x + c, & x \ge 1 \end{cases} \). Find the value of \( c \) so that \(\lim_{{x \to 1^-}} p(x) = \lim_{{x \to 1^+}} p(x)\).** **Graph Explanation:** The graph is a plot of \( g(x) \) with marked intervals and key points, indicating values relevant for evaluating the limits and function values. Pay close attention to identifying points of discontinuity, local extrema, and where the graph approaches vertical or horizontal asymptotes. This content is intended to guide students in evaluating functions and limits, interpreting piecewise functions, and finding specific values that ensure continuity.
Transcribed Image Text:**Evaluate each expression using the graph of \( g(x) \) shown, assuming the scale is 1. If a value does not exist, write "DNE."** a. \( g(0) \) b. \( g(2) \) c. \(\lim_{{x \to 0}} g(x)\) d. \(\lim_{{x \to 2^-}} g(x)\) e. \(\lim_{{x \to 2^+}} g(x)\) f. \(\lim_{{x \to 2}} g(x)\) The graph provided is a piecewise curve with multiple direction changes and special points, indicating possible local maximums, minimums, and discontinuities. The x-values particularly relevant for this problem include 0 and 2. **Let \( f(x) = \begin{cases} x^2 + 2x - 1, & x < 2 \\ x^3 - 9, & x > 2 \end{cases} \). Evaluate each expression below. If a value does not exist, write "DNE."** a. \( f(2) \) b. \(\lim_{{x \to 2^-}} f(x)\) c. \(\lim_{{x \to 2^+}} f(x)\) **Let \( p(x) = \begin{cases} 4-x, & x < 1 \\ -x + c, & x \ge 1 \end{cases} \). Find the value of \( c \) so that \(\lim_{{x \to 1^-}} p(x) = \lim_{{x \to 1^+}} p(x)\).** **Graph Explanation:** The graph is a plot of \( g(x) \) with marked intervals and key points, indicating values relevant for evaluating the limits and function values. Pay close attention to identifying points of discontinuity, local extrema, and where the graph approaches vertical or horizontal asymptotes. This content is intended to guide students in evaluating functions and limits, interpreting piecewise functions, and finding specific values that ensure continuity.
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