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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![**Transcription for Educational Use:**
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**Evaluate the given limit algebraically, if it exists.**
\[ \lim_{{x \to 0}} \frac{{\sin 8x}}{{6x - 2x^3}} \]
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**Explanation:**
This problem requires finding the limit of a function as \( x \) approaches 0. The function given is a rational expression with the sine of \( 8x \) in the numerator and a polynomial \( 6x - 2x^3 \) in the denominator. Solving this problem involves applying techniques from calculus, possibly L'Hôpital's Rule or series expansions, to evaluate the expression as \( x \) approaches 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc4bd04-a070-4f0a-8c81-81114a590c8c%2F3c406ffb-3768-4021-b97c-e3059ccbab91%2Fl0guxlp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Use:**
---
**Evaluate the given limit algebraically, if it exists.**
\[ \lim_{{x \to 0}} \frac{{\sin 8x}}{{6x - 2x^3}} \]
---
**Explanation:**
This problem requires finding the limit of a function as \( x \) approaches 0. The function given is a rational expression with the sine of \( 8x \) in the numerator and a polynomial \( 6x - 2x^3 \) in the denominator. Solving this problem involves applying techniques from calculus, possibly L'Hôpital's Rule or series expansions, to evaluate the expression as \( x \) approaches 0.
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