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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Answered: 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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