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1. Consider the given piecewise function f(x), find the limits at the given values. State if the limit does not exist. lim f(x) : а. x→2- b. lim f(x) : x→2+ 2 C. lim (x) = -3 -2 -1 1 -3

1. Consider the given piecewise function f(x), find the limits at the given values. State if the limit does not exist. lim f(x) : а. x→2- b. lim f(x) : x→2+ 2 C. lim (x) = -3 -2 -1 1 -3

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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1. Consider the given piecewise function \( f(x) \), find the limits at the given values. State if the limit does not exist. a. \(\lim_{{x \to 2^-}} f(x) = \underline{\ \ \ \ \ \ }\) b. \(\lim_{{x \to 2^+}} f(x) = \underline{\ \ \ \ \ \ }\) c. \(\lim_{{x \to 2}} f(x) = \underline{\ \ \ \ \ \ }\) **Graph Description:** The graph depicts a piecewise function with two linear segments: - The first segment (depicted in red) is a line with a positive slope. It originates below the y-axis and extends upward to the point \((2, 6)\), where there is an open circle, indicating that the point is not included in the segment. - The second segment (depicted in blue) is a line with a negative slope. It starts at the point \((2, -2)\) with a closed circle, signifying inclusion, and extends downward and to the right. This piecewise graph suggests different behavior of \( f(x) \) as \( x \) approaches 2 from the left and from the right.
Transcribed Image Text:1. Consider the given piecewise function \( f(x) \), find the limits at the given values. State if the limit does not exist. a. \(\lim_{{x \to 2^-}} f(x) = \underline{\ \ \ \ \ \ }\) b. \(\lim_{{x \to 2^+}} f(x) = \underline{\ \ \ \ \ \ }\) c. \(\lim_{{x \to 2}} f(x) = \underline{\ \ \ \ \ \ }\) **Graph Description:** The graph depicts a piecewise function with two linear segments: - The first segment (depicted in red) is a line with a positive slope. It originates below the y-axis and extends upward to the point \((2, 6)\), where there is an open circle, indicating that the point is not included in the segment. - The second segment (depicted in blue) is a line with a negative slope. It starts at the point \((2, -2)\) with a closed circle, signifying inclusion, and extends downward and to the right. This piecewise graph suggests different behavior of \( f(x) \) as \( x \) approaches 2 from the left and from the right.
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