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Series: Calculus: L'Hopital's Rule

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About this Series

  • Lessons: 8
  • Total Time: 1h 22m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/30/2009
  • Last Updated At: 06/01/2011

In this 8-lesson series, we'll look at indeterminate quotients and other indeterminate forms.

When taking limits, sometimes you will encounter expressions whose meanings can be interpreted in different ways. These limits are called indeterminate forms. A limit of a function is called an indeterminate form when it produces a mathematically meaningless expression. Indeterminate forms are also called indeterminant forms. In this four-lesson series, we'll look at basic indeterminate forms and how L'Hopital's rule helps us to evaluate them. The two types of indeterminate forms we'll focus on are 0/0 and infinity/infinity. Some indeterminate forms can be solved by using algebra tricks such as canceling or dividing by the highest power of x. Some expressions, however are camouflaged indeterminate forms that needs to be manipulated using mathematical identities or properties in order to establish that they are indeterminate.

L'Hopital's rule enables you to evaluate indeterminate forms quickly by using derivatives. When evaluating a limit, it is always a good idea to plug in the value first. If the result yields an indeterminate form, then use L'Hopital's rule. As long as the limit is still an indeterminate form you can reuse L'Hopital's rule. L'Hopital's rule might not produce the right answer if you use it on a limit that does not produce an indeterminate form.

As long as the limit still produces an indeterminate form you can reuse L'Hopital's rule. When applying L'Hopital's rule to a quotient containing one or more products or compositions of functions, it is necessary to use the product or chain rules. L'Hopital's rule, however, might not give you the right answer if you use it on a limit that does not produce an indeterminate form.

Sometimes, we can use mathematical identities or properties to manipulate or re-state an expression such that we can verify that it is an indeterminate form. A limit of a function is called an indeterminate form when it produces a mathematically meaningless expression. Indeterminate forms are also called indeterminant forms.

In these lessons, we'll look at indeterminate products (e.g. 0 times infinity) and indeterminate differences. We'll also use properties of logarithms to restate things like 1^infinity in order to find an indeterminate form that we can the apply L'Hopital's rule to.

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

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Thinkwell
Thinkwell
2174 lessons
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Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

Nopic_tan
Thought the video was great
11/15/2010
~ Stephen22

Very helpful for me as I plunge forward in Calc 2. For some reason I was making a minor mistake differentiating the ln(f(x)) portion of this problem. Good to always make sure you are placing items correctly in the numerator or denominator. I was working on a similar problem that was the same except it was 3/x instead of 1/x. Of course the answer is still e! Thanks!

Below are the descriptions for each of the lessons included in the series:

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