1 – x6 (d) lim x→0 1 – cos (x6) ||

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 problem states:

\( (d) \, \lim_{{x \to 0}} \frac{{1 - x^6}}{{1 - \cos(x^6)}} = \)

This is a limit problem where you need to evaluate the expression as \( x \) approaches 0. 

To solve this, you may need to apply L'Hôpital's Rule or use a Taylor series expansion for \( \cos(x) \) near 0, which is:

\[ \cos(x) \approx 1 - \frac{x^2}{2} + \frac{x^4}{24} - \cdots \]

Using this expansion can simplify the limit calculation.
Transcribed Image Text:The problem states: \( (d) \, \lim_{{x \to 0}} \frac{{1 - x^6}}{{1 - \cos(x^6)}} = \) This is a limit problem where you need to evaluate the expression as \( x \) approaches 0. To solve this, you may need to apply L'Hôpital's Rule or use a Taylor series expansion for \( \cos(x) \) near 0, which is: \[ \cos(x) \approx 1 - \frac{x^2}{2} + \frac{x^4}{24} - \cdots \] Using this expansion can simplify the limit calculation.
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