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2. lim √xe-2x² x→∞x = or

2. lim √xe-2x² x→∞x = or

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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**Mathematics Problems for Optimization and Limits** 1. **Optimization Problem:** - A box with a square base without a lid must have a volume of 32,000. Find the dimensions of the box that minimize the amount of material used. 2. **Limit Problem 1:** - \(\lim_{{x \to \infty}} \sqrt{x} e^{-2x^2} =\) 3. **Limit Problem 2:** - \(\lim_{{x \to 0}} \frac{{\cos 2x - \cos 25x}}{{x^2 - 2x}} =\) 4. **Limit Problem 3:** - \(\lim_{{x \to 0}} x \ln x^2 =\) 5. **Area Calculation:** - Find the area between \(y = \cos 2x\) and \(y = \sin 2x\), over the interval \([0, \pi]\). These problems involve concepts such as optimization, calculus limits, and area calculations in mathematics, and are designed to challenge students' understanding of these topics.
Transcribed Image Text:**Mathematics Problems for Optimization and Limits** 1. **Optimization Problem:** - A box with a square base without a lid must have a volume of 32,000. Find the dimensions of the box that minimize the amount of material used. 2. **Limit Problem 1:** - \(\lim_{{x \to \infty}} \sqrt{x} e^{-2x^2} =\) 3. **Limit Problem 2:** - \(\lim_{{x \to 0}} \frac{{\cos 2x - \cos 25x}}{{x^2 - 2x}} =\) 4. **Limit Problem 3:** - \(\lim_{{x \to 0}} x \ln x^2 =\) 5. **Area Calculation:** - Find the area between \(y = \cos 2x\) and \(y = \sin 2x\), over the interval \([0, \pi]\). These problems involve concepts such as optimization, calculus limits, and area calculations in mathematics, and are designed to challenge students' understanding of these topics.
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