Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Use L' Hopital's Rule if possible, to evaluate the following limits.

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The image shows a mathematical expression to be solved as a limit problem: a) \(\lim_{{x \to \infty}} \frac{e^{x^2}}{x^2}\) This expression represents the limit of the function \(\frac{e^{x^2}}{x^2}\) as \(x\) approaches infinity. The limit evaluates how the function behaves as \(x\) becomes very large.
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Transcribed Image Text:The image shows a mathematical expression to be solved as a limit problem: a) \(\lim_{{x \to \infty}} \frac{e^{x^2}}{x^2}\) This expression represents the limit of the function \(\frac{e^{x^2}}{x^2}\) as \(x\) approaches infinity. The limit evaluates how the function behaves as \(x\) becomes very large.
b) \(\lim_{{x \to 0^+}} \left( \cot x - \frac{1}{x} \right)\) In this expression, we are finding the limit of the function \(\cot x - \frac{1}{x}\) as \(x\) approaches \(0\) from the positive side.
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Transcribed Image Text:b) \(\lim_{{x \to 0^+}} \left( \cot x - \frac{1}{x} \right)\) In this expression, we are finding the limit of the function \(\cot x - \frac{1}{x}\) as \(x\) approaches \(0\) from the positive side.
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