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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evaluate the following limit
![The expression shown in the image is a mathematical limit. It is written as follows:
\[ \lim_{{x \to 5}} \frac{\frac{1}{5} + \frac{1}{x}}{5 + x} \]
This limit notation indicates that we are interested in finding the value that the function \(\frac{\frac{1}{5} + \frac{1}{x}}{5 + x}\) approaches as \(x\) approaches 5.
To evaluate this limit, one would typically substitute values of \(x\) that are very close to 5 and analyze the behavior of the function. This can involve algebraic simplifications, numerical approximations, or, for more complex functions, applying limit theorems or L'Hôpital's rule if applicable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe7817cb-5274-4434-90ec-13ab480c973d%2F95d2044e-aea6-499c-bf48-89be5c5f3c0e%2Fpe0m4h9_processed.png&w=3840&q=75)
Transcribed Image Text:The expression shown in the image is a mathematical limit. It is written as follows:
\[ \lim_{{x \to 5}} \frac{\frac{1}{5} + \frac{1}{x}}{5 + x} \]
This limit notation indicates that we are interested in finding the value that the function \(\frac{\frac{1}{5} + \frac{1}{x}}{5 + x}\) approaches as \(x\) approaches 5.
To evaluate this limit, one would typically substitute values of \(x\) that are very close to 5 and analyze the behavior of the function. This can involve algebraic simplifications, numerical approximations, or, for more complex functions, applying limit theorems or L'Hôpital's rule if applicable.
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