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...
Related questions
Question
![### Evaluating Limits Using Algebraic Manipulations and Limit Laws
In this section, we will learn how to use algebraic manipulations and limit laws to evaluate the following limits:
#### (a) Problem:
\[ \lim_{{x \to \infty}} \left( \sqrt{x + 9} - \sqrt{x} \right) \]
#### (b) Problem:
\[ \lim_{{x \to 3}} \frac{(x + 1)^7 (x - 1)^5}{(x - 4)^3 (x + 3)^2} \]
In problem (a), we will explore techniques to simplify the expression involving square roots as \(x\) approaches infinity. For problem (b), we will deal with a limit that approaches a finite value and involves the manipulation of polynomial expressions in the numerator and denominator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa589a0b1-5940-47b0-b798-8fa24b0ff23c%2F2c5616d7-fbcd-4579-9f34-8f2eab58f6e2%2Fuk3ma7l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluating Limits Using Algebraic Manipulations and Limit Laws
In this section, we will learn how to use algebraic manipulations and limit laws to evaluate the following limits:
#### (a) Problem:
\[ \lim_{{x \to \infty}} \left( \sqrt{x + 9} - \sqrt{x} \right) \]
#### (b) Problem:
\[ \lim_{{x \to 3}} \frac{(x + 1)^7 (x - 1)^5}{(x - 4)^3 (x + 3)^2} \]
In problem (a), we will explore techniques to simplify the expression involving square roots as \(x\) approaches infinity. For problem (b), we will deal with a limit that approaches a finite value and involves the manipulation of polynomial expressions in the numerator and denominator.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning