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Problem

Suppose $ f $ is a positive function. If $ lim_{x…

01:12

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Problem 85 Hard Difficulty

Evaluate
$$ \displaystyle \lim_{x\to \infty} \left[ x - x^2 \ln \left( \frac{1 + x}{x} \right) \right] $$.

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01:46

Wen Zheng

00:51

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Related Topics

Derivatives

Differentiation

Volume

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04:35

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

this problem, we're gonna be taking the limit as X goes to infinity. But we're going to want to rewrite the given limit and apply a substitution. We're gonna let you equals one over X. So using all of this um substitution, we end up getting it into the form of the limit as X goes to infinity of x minus x squared, I'm the natural law of one over X plus one. Then based on this we end up getting when we plug in U. Equals zero, we get 0/0. So we're gonna have to use local tiles. Rule a substituting you where we can we get one minus one over you plus one and then that's all gonna be over to you. Then Roy plug in zero here. And simplify further. We get um one over two times u plus one, plugging in zero. We get 1/2. So one half is going to be the limit for this function.

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Calculus: Early Transcendentals

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Related Topics

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Video Thumbnail

04:35

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Video Thumbnail

06:14

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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