Limits 1. Below is a graph of the function g(x), find each limit as listed below. If the limit does not exist, provide that as your answer. -5 -4 -3 -2 a. lim g(x) = x→-4 b. lim g(x) = x→2 c. lim g(x) = x→4 Y 3 2 1 0 -1 D 1 -1 -2 -3 3 4 I
Limits 1. Below is a graph of the function g(x), find each limit as listed below. If the limit does not exist, provide that as your answer. -5 -4 -3 -2 a. lim g(x) = x→-4 b. lim g(x) = x→2 c. lim g(x) = x→4 Y 3 2 1 0 -1 D 1 -1 -2 -3 3 4 I
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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Question
![### Limits
1. Below is a graph of the function \( g(x) \). Find each limit as listed below. If the limit does not exist, provide that as your answer.
#### Graph Explanation
- The graph shows the function \( g(x) \) plotted on a coordinate plane.
- The x-axis ranges from -6 to 6, while the y-axis ranges from -4 to 3.
- The function exhibits several key features, such as peaks, troughs, and a gap at \( x = 3 \).
#### Limits to Find:
a. \( \lim_{{x \to -4}} g(x) = \)
b. \( \lim_{{x \to 2}} g(x) = \)
c. \( \lim_{{x \to 4}} g(x) = \)
2. Find the following limit, show your work:
\[
\lim_{{h \to 0}} \frac{{(5-h)^2 - 25}}{h}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0685efca-60cb-46ac-abbc-f745cca97923%2F57a0691a-ba50-4a6c-8e0f-d396a2012ee7%2Fvv5vjbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Limits
1. Below is a graph of the function \( g(x) \). Find each limit as listed below. If the limit does not exist, provide that as your answer.
#### Graph Explanation
- The graph shows the function \( g(x) \) plotted on a coordinate plane.
- The x-axis ranges from -6 to 6, while the y-axis ranges from -4 to 3.
- The function exhibits several key features, such as peaks, troughs, and a gap at \( x = 3 \).
#### Limits to Find:
a. \( \lim_{{x \to -4}} g(x) = \)
b. \( \lim_{{x \to 2}} g(x) = \)
c. \( \lim_{{x \to 4}} g(x) = \)
2. Find the following limit, show your work:
\[
\lim_{{h \to 0}} \frac{{(5-h)^2 - 25}}{h}
\]
Expert Solution
Step 1
Graph for a function is given.
To find :
Limit of a function is defined as the value to which a function approaches as approaches some value.
The left hand limit of a function is defined as the value to which a function approaches when variable approaches the limit from the left.
The right hand limit of a function is defined as the value to which a function approaches when variables approaches the limit from the right.
Limit of a function exists only when left hand limit equals to the right hand limit.
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