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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![**Finding Limits Algebraically**
**Problem:**
Find the limit algebraically:
\[
\lim_{{x \to 121}} \frac{{\sqrt{x} - 11}}{{4(x - 121)}}
\]
**Explanation:**
To solve this limit, one might consider rationalizing the expression, using algebraic manipulations to simplify the function, or recognizing any special algebraic forms that can assist in evaluating the limit as \( x \) approaches 121. This is particularly useful when the direct substitution leads to an indeterminate form like \(\frac{0}{0}\).
This step typically involves manipulating the function into a form where the limit can be evaluated without resulting in indeterminate expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54e8c682-be67-4ef0-bd1d-cf8b2e543b76%2F1bf9568b-687b-401a-a1fb-346002512a71%2Fqlzw71c_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding Limits Algebraically**
**Problem:**
Find the limit algebraically:
\[
\lim_{{x \to 121}} \frac{{\sqrt{x} - 11}}{{4(x - 121)}}
\]
**Explanation:**
To solve this limit, one might consider rationalizing the expression, using algebraic manipulations to simplify the function, or recognizing any special algebraic forms that can assist in evaluating the limit as \( x \) approaches 121. This is particularly useful when the direct substitution leads to an indeterminate form like \(\frac{0}{0}\).
This step typically involves manipulating the function into a form where the limit can be evaluated without resulting in indeterminate expressions.
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