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 limit
![The image displays a mathematical expression for finding the limit as \( x \) approaches infinity. The expression is:
\[
\lim_{{x \to \infty}} \frac{{4x^{\frac{3}{2}}}}{{7x^{\frac{3}{2}} + 8}}
\]
In this expression, the function in the numerator is \( 4x^{\frac{3}{2}} \) and in the denominator is \( 7x^{\frac{3}{2}} + 8 \). This limit evaluates the behavior of the function as \( x \) becomes very large.
To solve this limit, you would typically compare the degrees of the polynomial in the numerator and the denominator. Since both have the same degree, you can determine the limit by looking at the leading coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb37dcdcd-0ea6-4523-b03b-c2bd2641954c%2Fd8c677ff-1e27-4ed1-9f9d-b6c12d71d8e1%2F08fywqt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a mathematical expression for finding the limit as \( x \) approaches infinity. The expression is:
\[
\lim_{{x \to \infty}} \frac{{4x^{\frac{3}{2}}}}{{7x^{\frac{3}{2}} + 8}}
\]
In this expression, the function in the numerator is \( 4x^{\frac{3}{2}} \) and in the denominator is \( 7x^{\frac{3}{2}} + 8 \). This limit evaluates the behavior of the function as \( x \) becomes very large.
To solve this limit, you would typically compare the degrees of the polynomial in the numerator and the denominator. Since both have the same degree, you can determine the limit by looking at the leading coefficients.
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