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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![### Example Solution for a Limits Problem
Consider the following limit problem:
\[ \lim_{{x \to 7^-}} \ln(7 - x) \]
To solve this limit, we need to understand the behavior of the natural logarithm function, \( \ln \), as its argument approaches zero from the positive side.
The expression inside the natural logarithm, \( 7 - x \), approaches zero as \( x \) approaches 7 from the left (i.e., for values of \( x \) less than 7).
So, we rewrite the problem as:
\[ \lim_{{x \to 7^-}} \ln(7 - x) \]
Since \( \ln(y) \) approached \(-\infty\) as \( y \) approached zero from the positive side (y > 0), our limit becomes:
\[ \lim_{{y \to 0^+}} \ln(y) = -\infty \]
Therefore, the limit is:
\[ \lim_{{x \to 7^-}} \ln(7 - x) = -\infty \]
Thus, the final answer to this limit problem is \( -\infty \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa451162e-14ac-4cfd-a2c6-1eae7f4a5f1a%2F5b916c67-49aa-48b0-8496-f12626cf1c4f%2Fqw9qb5w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Example Solution for a Limits Problem
Consider the following limit problem:
\[ \lim_{{x \to 7^-}} \ln(7 - x) \]
To solve this limit, we need to understand the behavior of the natural logarithm function, \( \ln \), as its argument approaches zero from the positive side.
The expression inside the natural logarithm, \( 7 - x \), approaches zero as \( x \) approaches 7 from the left (i.e., for values of \( x \) less than 7).
So, we rewrite the problem as:
\[ \lim_{{x \to 7^-}} \ln(7 - x) \]
Since \( \ln(y) \) approached \(-\infty\) as \( y \) approached zero from the positive side (y > 0), our limit becomes:
\[ \lim_{{y \to 0^+}} \ln(y) = -\infty \]
Therefore, the limit is:
\[ \lim_{{x \to 7^-}} \ln(7 - x) = -\infty \]
Thus, the final answer to this limit problem is \( -\infty \).
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