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Suppose $ f $ is a positive function. If $ lim_{x\to a} f(x) = 0 $ and $ lim_{x\to a} g(x) = \infty $, show that $$ \displaystyle \lim_{x\to a} [f(x)]^{g(x)} = 0 $$This shows that $ 0^{\infty} $ is not an indeterminate form.
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02:18
Wen Zheng
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 4
Indeterminate Forms and l'Hospital's Rule
Derivatives
Differentiation
Volume
Baylor University
University of Nottingham
Idaho State University
Boston College
Lectures
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A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.
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we know the first thing we can do is we can rewrite it in terms of natural log of why is G of axe times Ellen of f of axe to indicate the same thing? Because now we can more easily take the limit as extra purchase. A G evac stems the natural log of after wax, and we know this is equivalent to negative infinity. Now, given this we know the limit is ex purchase A of aftereffects of natural of affects is negative. Infinity and we know the woman is expertise have affects zero. Therefore, given this what we know is that we can rewrite this as the limit as Expro. Ches eh Eat the natural log of why we know this is the limit as H approaches negative infinity. You see, EJ, we know you did the negative. Infinity is simply going to be zero
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