L'Hopital's Rule

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•
Mathematics
•
11th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is L'Hopital's Rule?
Back
L'Hopital's Rule is a method in calculus used to evaluate limits of indeterminate forms, specifically 0/0 or ∞/∞, by differentiating the numerator and denominator.
2.
FLASHCARD QUESTION
Front
When can L'Hopital's Rule be applied?
Back
L'Hopital's Rule can be applied when evaluating limits that result in the indeterminate forms 0/0 or ∞/∞.
3.
FLASHCARD QUESTION
Front
State the formula for L'Hopital's Rule.
Back
If lim (x -> c) f(x) = 0 and lim (x -> c) g(x) = 0 (or both approach ∞), then: lim (x -> c) (f(x)/g(x)) = lim (x -> c) (f'(x)/g'(x)) provided the limit on the right exists.
4.
FLASHCARD QUESTION
Front
What is an indeterminate form?
Back
An indeterminate form is an expression that does not have a well-defined limit, such as 0/0, ∞/∞, 0×∞, ∞ - ∞, 0^0, ∞^0, and 1^∞.
5.
FLASHCARD QUESTION
Front
Give an example of a limit that can be solved using L'Hopital's Rule.
Back
lim (x -> 0) (sin(x)/x) = 1. This limit is of the form 0/0.
6.
FLASHCARD QUESTION
Front
What is the first step in applying L'Hopital's Rule?
Back
The first step is to confirm that the limit results in an indeterminate form (0/0 or ∞/∞).
7.
FLASHCARD QUESTION
Front
Can L'Hopital's Rule be applied multiple times?
Back
Yes, L'Hopital's Rule can be applied repeatedly if the resulting limit after the first application is still an indeterminate form.
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