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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![### Problem 384
Evaluate the limit:
\[
\lim_{{x \to 0}} \frac{{\sin x - x}}{{x^2}}
\]
This expression involves finding the limit of a fraction where the numerator is the difference between the sine of \( x \) and \( x \), and the denominator is \( x \) squared, as \( x \) approaches 0. This type of problem often requires the use of L'Hôpital's Rule or Taylor series expansion due to the indeterminate form \(\frac{0}{0}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1fe61787-87ec-42ef-9b74-8862c323e0b5%2Fb2ae53cc-00ab-4bba-9ffa-8b6ead0f4f88%2F7d5o12q_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 384
Evaluate the limit:
\[
\lim_{{x \to 0}} \frac{{\sin x - x}}{{x^2}}
\]
This expression involves finding the limit of a fraction where the numerator is the difference between the sine of \( x \) and \( x \), and the denominator is \( x \) squared, as \( x \) approaches 0. This type of problem often requires the use of L'Hôpital's Rule or Taylor series expansion due to the indeterminate form \(\frac{0}{0}\).
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