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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![### Limit Calculation Using Limit Rules
Given:
\[ \lim_{x \to 8} f(x) = 9 \]
Use the limit rules to find the following limit:
\[ \lim_{x \to 8} \sqrt{f(x)} \]
### Solution:
Using the limit rule that allows the combination of the limit of a function inside a continuous function, we can proceed as follows:
Given:
\[ \lim_{x \to 8} f(x) = 9 \]
We need to find:
\[ \lim_{x \to 8} \sqrt{f(x)} \]
Since the square root function is continuous, we can write:
\[ \sqrt{\lim_{x \to 8} f(x)} \]
Substituting the known limit:
\[ \sqrt{9} = 3 \]
Therefore:
\[ \lim_{x \to 8} \sqrt{f(x)} = 3 \]
So, the limit is 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90eda9e3-028c-4bf5-879e-83d805099bfb%2Ff42dcb79-0cb8-4ad3-b7b3-290f6e1eeeb1%2Ftm3p4ko_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Limit Calculation Using Limit Rules
Given:
\[ \lim_{x \to 8} f(x) = 9 \]
Use the limit rules to find the following limit:
\[ \lim_{x \to 8} \sqrt{f(x)} \]
### Solution:
Using the limit rule that allows the combination of the limit of a function inside a continuous function, we can proceed as follows:
Given:
\[ \lim_{x \to 8} f(x) = 9 \]
We need to find:
\[ \lim_{x \to 8} \sqrt{f(x)} \]
Since the square root function is continuous, we can write:
\[ \sqrt{\lim_{x \to 8} f(x)} \]
Substituting the known limit:
\[ \sqrt{9} = 3 \]
Therefore:
\[ \lim_{x \to 8} \sqrt{f(x)} = 3 \]
So, the limit is 3.
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