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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa55013e1-91aa-48be-9c4b-bf8a0e47de22%2Fc63ab8cf-0257-48cb-ba40-a76473587fae%2F5s4wkh4_processed.png&w=3840&q=75)
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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