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(b) lim (cos ()) I-1 COS

(b) lim (cos ()) I-1 COS

Calculus: Early Transcendentals
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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(b) \(\lim_{x \to 1} \left( \cos \left( \frac{\pi}{2} x \right) \right)^{x-1}\) This mathematical expression represents the limit of a function as \(x\) approaches 1. The function is \(\left( \cos \left( \frac{\pi}{2} x \right) \right)^{x-1}\). **Explanation:** - **Cosine Function:** The cosine of \(\frac{\pi}{2} x\) is evaluated inside the parentheses. The cosine function oscillates between -1 and 1, and \(\frac{\pi}{2} x\) introduces a transformation to the angle. - **Exponent:** The result of the cosine function is raised to the power of \(x - 1\). In this limit problem, you'll evaluate how the function behaves as \(x\) gets very close to 1.
Transcribed Image Text:(b) \(\lim_{x \to 1} \left( \cos \left( \frac{\pi}{2} x \right) \right)^{x-1}\) This mathematical expression represents the limit of a function as \(x\) approaches 1. The function is \(\left( \cos \left( \frac{\pi}{2} x \right) \right)^{x-1}\). **Explanation:** - **Cosine Function:** The cosine of \(\frac{\pi}{2} x\) is evaluated inside the parentheses. The cosine function oscillates between -1 and 1, and \(\frac{\pi}{2} x\) introduces a transformation to the angle. - **Exponent:** The result of the cosine function is raised to the power of \(x - 1\). In this limit problem, you'll evaluate how the function behaves as \(x\) gets very close to 1.
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