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Use the graph to decide whether the value of the given quantity exists, If it does find it. If not, cxplain why. (a) f(1) (b) lim /(x) (e) S(4) (d) lim f(x)

Use the graph to decide whether the value of the given quantity exists, If it does find it. If not, cxplain why. (a) f(1) (b) lim /(x) (e) S(4) (d) lim f(x)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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I know Bartleby has a limit on three parts, so if you have to only do three, please show me how to do A, B, and D. Thank you.

### Understanding Function Values and Limits Using a Graph This exercise encourages students to use the provided graph to determine whether specific function values and limits exist. If they do, they are expected to find the values; if not, students should explain why. #### Questions: (a) \( f(1) \) (b) \( \lim_{{x \to 2}} f(x) \) (c) \( f(4) \) (d) \( \lim_{{x \to 4}} f(x) \) #### Graph Analysis: In the provided graph: - The \( x \)-axis ranges from -1 to 6. - The \( y \)-axis ranges from 0 to 6. - There appears to be a function \( f(x) \) graphed along the coordinate system, depicted as a curve. ### Detailed Explanation of the Graph: - For \( x = 1 \), locate the corresponding \( y \)-value on the function's curve. - For \( x \to 2 \), determine the limit of \( f(x) \) by observing the behavior of the function as it approaches \( x = 2 \) from both the left-hand and right-hand sides. - For \( x = 4 \), assess the function's value directly on the curve. - For \( x \to 4 \), determine the limit by observing how the function behaves as \( x \) approaches 4 from both sides. Students should pay close attention to any breaks, holes, or discontinuities in the graph, as these often indicate where certain values or limits may not exist. When a function value doesn't match its limit at a particular point, it often suggests a discontinuity at that point.
Transcribed Image Text:### Understanding Function Values and Limits Using a Graph This exercise encourages students to use the provided graph to determine whether specific function values and limits exist. If they do, they are expected to find the values; if not, students should explain why. #### Questions: (a) \( f(1) \) (b) \( \lim_{{x \to 2}} f(x) \) (c) \( f(4) \) (d) \( \lim_{{x \to 4}} f(x) \) #### Graph Analysis: In the provided graph: - The \( x \)-axis ranges from -1 to 6. - The \( y \)-axis ranges from 0 to 6. - There appears to be a function \( f(x) \) graphed along the coordinate system, depicted as a curve. ### Detailed Explanation of the Graph: - For \( x = 1 \), locate the corresponding \( y \)-value on the function's curve. - For \( x \to 2 \), determine the limit of \( f(x) \) by observing the behavior of the function as it approaches \( x = 2 \) from both the left-hand and right-hand sides. - For \( x = 4 \), assess the function's value directly on the curve. - For \( x \to 4 \), determine the limit by observing how the function behaves as \( x \) approaches 4 from both sides. Students should pay close attention to any breaks, holes, or discontinuities in the graph, as these often indicate where certain values or limits may not exist. When a function value doesn't match its limit at a particular point, it often suggests a discontinuity at that point.
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