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Problem

If $ f' $ is continuous, $ f(2) = 0 $, and $ f'(2…

01:24

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Problem 86 Hard Difficulty

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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WZ

Wen Zheng

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Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

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Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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Video Transcript

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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Video Thumbnail

06:14

Review

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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