Indeterminate Forms and L'Hopital's Rule
This lesson covers indeterminate forms in calculus, including 0/0, infinity/infinity, 0, infinity, 1^infinity, 0^0, infinity^0, and infinity - infinity. The lesson also introduces L'Hopital's Rule, which is used to calculate indeterminate forms. The transcript includes several examples of how to use L'Hopital's Rule to find limits of functions. Additionally, the lesson covers indeterminate exponential forms and how to convert them to other indeterminate forms in order to find their limits.
Indeterminate forms 0/0, infinity/infinity, 0, infinity, 1^infinity, 0^0, infinity^0, and infinity - infinity. L'Hopital's Rule.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- What are indeterminate forms?
- What is L'Hopital's Rule?
- How do you use L'Hopital's Rule?
- When is a limit indeterminate?
- What is the limit as x approaches 0 of xlnx?
- What are the limit properties of lnx and e^x?
- What are exponential forms?
- How do you find the limit of x^1/x as x goes to infinity?
- What is the limit of x^x as x goes to 0?
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Staff Review
This video is crucial to taking many limits in Calculus. Indeterminate forms are introduced and discussed. The forms are 0/0, infinity / infinity, and 0*infinity. LâHopitalâs rule is the method used to calculate the limit of these indeterminate forms. The limit properties of lnx and e^x are also shown. Exponential forms 1^infinity, 0^0, and infinity^0 are explained as well. Finally, the form infinity - infinity is discussed.
