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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![The expression shown is a calculus problem related to limits. The problem is to find the limit as \( x \) approaches infinity for the following expression:
\[ b) \lim_{{x \to \infty}} \frac{2x^2 + \cos(3x)}{x^2 - 10x + \cos x} \]
**Explanation for Educational Context:**
The limit evaluates the behavior of the given rational function as the variable \( x \) tends towards infinity. The expression consists of a polynomial and trigonometric functions in both the numerator and the denominator. This problem is typical in calculus where students learn to analyze the dominant terms in rational functions and evaluate their limits. The polynomial terms in \( x^2 \) will govern the behavior of the function more significantly than the trigonometric terms as \( x \) becomes very large.
Students would need to apply algebraic techniques or L'Hopital's rule to evaluate the limit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89102401-f01a-4d56-b747-11e6ab188921%2Fcd607da3-e20c-429a-919f-7c06d5c23e9b%2F3qtshh_processed.png&w=3840&q=75)
Transcribed Image Text:The expression shown is a calculus problem related to limits. The problem is to find the limit as \( x \) approaches infinity for the following expression:
\[ b) \lim_{{x \to \infty}} \frac{2x^2 + \cos(3x)}{x^2 - 10x + \cos x} \]
**Explanation for Educational Context:**
The limit evaluates the behavior of the given rational function as the variable \( x \) tends towards infinity. The expression consists of a polynomial and trigonometric functions in both the numerator and the denominator. This problem is typical in calculus where students learn to analyze the dominant terms in rational functions and evaluate their limits. The polynomial terms in \( x^2 \) will govern the behavior of the function more significantly than the trigonometric terms as \( x \) becomes very large.
Students would need to apply algebraic techniques or L'Hopital's rule to evaluate the limit.
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