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11) Using the function y = (x) as shown below, find the value of each of the following: lim f(x)= d. (1) = а. b. lim f(x)= x→1* е. x→-3 lim f(x) С. lim f(x)= x→1 y -3 -2 -1 to

11) Using the function y = (x) as shown below, find the value of each of the following: lim f(x)= d. (1) = а. b. lim f(x)= x→1* е. x→-3 lim f(x) С. lim f(x)= x→1 y -3 -2 -1 to

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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### Educational Website Content: Calculus - Evaluating Limits and Function Values #### Problem 11: Using the Function \( y = f(x) \) Using the function \( y = f(x) \) as shown below, find the value of each of the following: a. \( \lim_{{x \to 1^-}} f(x) = \) b. \( \lim_{{x \to 1^+}} f(x) = \) c. \( \lim_{{x \to 1}} f(x) = \) d. \( f(1) = \) e. \( \lim_{{x \to 3}} f(x) = \) #### Graph Description: The graph provided depicts the function \( f(x) \) on a Cartesian plane. The x-axis is labeled from -4 to 6, and the y-axis is labeled from -2 to 4. Important points are marked on the graph, which are critical for evaluating the limits and the function values. Below is a detailed description of significant points and behaviors of the graph: - At \( x = -3 \), \( f(x) = 0 \). - At \( x = -2 \), \( f(x) = 4 \). - At \( x = -1 \), \( f(x) = 2 \). - The graph is undefined at \( x = 1 \), but limits from both directions need to be considered. - From left to right at \( x = 1 \), the function approaches \( f(x) = 2 \) as x approaches 1 from the left, and \( f(x) = 0 \) as x approaches 1 from the right. - At \( x = 2 \), \( f(x) = 1 \). - At \( x = 3 \), the function is undefined; however, both one-sided limits need to be evaluated. - From the left and right of \( x = 3 \), the graph approaches the value \( 1 \). - At \( x = 4 \), \( f(x) = 2 \). - At \( x = 5 \), \( f(x) = 1 \). - At \( x = 6 \), the function appears undefined from the graph. #### Evaluations: Based on the graph, the following values can be determined: a. \( \lim_{{x \to
Transcribed Image Text:### Educational Website Content: Calculus - Evaluating Limits and Function Values #### Problem 11: Using the Function \( y = f(x) \) Using the function \( y = f(x) \) as shown below, find the value of each of the following: a. \( \lim_{{x \to 1^-}} f(x) = \) b. \( \lim_{{x \to 1^+}} f(x) = \) c. \( \lim_{{x \to 1}} f(x) = \) d. \( f(1) = \) e. \( \lim_{{x \to 3}} f(x) = \) #### Graph Description: The graph provided depicts the function \( f(x) \) on a Cartesian plane. The x-axis is labeled from -4 to 6, and the y-axis is labeled from -2 to 4. Important points are marked on the graph, which are critical for evaluating the limits and the function values. Below is a detailed description of significant points and behaviors of the graph: - At \( x = -3 \), \( f(x) = 0 \). - At \( x = -2 \), \( f(x) = 4 \). - At \( x = -1 \), \( f(x) = 2 \). - The graph is undefined at \( x = 1 \), but limits from both directions need to be considered. - From left to right at \( x = 1 \), the function approaches \( f(x) = 2 \) as x approaches 1 from the left, and \( f(x) = 0 \) as x approaches 1 from the right. - At \( x = 2 \), \( f(x) = 1 \). - At \( x = 3 \), the function is undefined; however, both one-sided limits need to be evaluated. - From the left and right of \( x = 3 \), the graph approaches the value \( 1 \). - At \( x = 4 \), \( f(x) = 2 \). - At \( x = 5 \), \( f(x) = 1 \). - At \( x = 6 \), the function appears undefined from the graph. #### Evaluations: Based on the graph, the following values can be determined: a. \( \lim_{{x \to
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