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Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. If l'Hospital's Rule doesn't apply, explain why.

$ \displaystyle \lim_{x\to 0^+} \left(\frac{1}{x} - \frac{1}{\tan^{-1} x} \right) $

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03:07

Wen Zheng

00:48

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 4

Indeterminate Forms and l'Hospital's Rule

Derivatives

Differentiation

Volume

Missouri State University

Harvey Mudd College

Baylor University

Boston College

Lectures

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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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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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Find the limit. Use l'…

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for this problem, we see that if we take the limit of our function are given, function is one over x minus one over the inverse tangent X. But we're going to rewrite this as the arc tangent of x minus X. Try to buy the X times the ark tangent of acts. So what we do is we found a common denominator and combine them. This allows us to take the limit more easily. We see that when we take the limit as X approaches zero from the right, we get 0/0. So that's going to be an indeterminate form. That's okay though, because now each knees low tells role which ends up giving us 1/1 plus X squared minus one. And then on the bottom we'll end up getting are tangent X plus acts over one plus X squared. Now combining everything and taking the limit as X goes to zero from the right, We end up getting on here -2 times zero. We take the derivative again, we'll get negative two times zero, and then we'll get another. Um We'll get 0-plus two. So as a result of that, our final answer is going to be zero.

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