**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.

Given f(x)=-x2+2x-1, x<2x3-9 ,x>2(c)limx→2f(x)LHL limx→2-f(x)…

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

**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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