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
![### Limit Evaluation Problem
**Problem Statement:**
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
\[
\lim_{{x \to -6}} (5x - 7)
\]
Below the problem statement is a blank box where the answer should be entered.
### Explanation:
To evaluate the limit, substitute \( x = -6 \) directly into the function:
\[
5(-6) - 7 = -30 - 7 = -37
\]
Therefore, the limit is:
\[
\boxed{-37}
\]
If substituting \( x = -6 \) into the function resulted in an undefined expression, you would enter DNE (Does Not Exist) in the blank box.
In this case, the function is a linear polynomial, which is continuous everywhere, so it has a well-defined limit at \( x = -6 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29f44afc-13bd-4765-a69d-3ff085ad17f9%2F575cac31-89dc-41bd-922a-28ca93899a8b%2F3b9hl6k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Limit Evaluation Problem
**Problem Statement:**
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
\[
\lim_{{x \to -6}} (5x - 7)
\]
Below the problem statement is a blank box where the answer should be entered.
### Explanation:
To evaluate the limit, substitute \( x = -6 \) directly into the function:
\[
5(-6) - 7 = -30 - 7 = -37
\]
Therefore, the limit is:
\[
\boxed{-37}
\]
If substituting \( x = -6 \) into the function resulted in an undefined expression, you would enter DNE (Does Not Exist) in the blank box.
In this case, the function is a linear polynomial, which is continuous everywhere, so it has a well-defined limit at \( x = -6 \).
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