
L'hopital's rule
Flashcard
•
Mathematics
•
12th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is L'Hôpital's Rule?
Back
A method for finding limits of indeterminate forms (0/0 or ∞/∞) by differentiating the numerator and denominator.
2.
FLASHCARD QUESTION
Front
When can L'Hôpital's Rule be applied?
Back
It can be applied when evaluating limits that result in indeterminate forms such as 0/0 or ∞/∞.
3.
FLASHCARD QUESTION
Front
State the formula for L'Hôpital's Rule.
Back
If lim (x→c) f(x) = 0 and lim (x→c) g(x) = 0, then lim (x→c) (f(x)/g(x)) = lim (x→c) (f'(x)/g'(x)) if the limit on the right exists.
4.
FLASHCARD QUESTION
Front
What is an indeterminate form?
Back
An expression that does not have a well-defined limit, such as 0/0 or ∞/∞.
5.
FLASHCARD QUESTION
Front
Provide an example of a limit that can be solved using L'Hôpital's Rule: lim (x→0) (sin x)/x.
Back
The limit evaluates to 1 using L'Hôpital's Rule.
6.
FLASHCARD QUESTION
Front
What is the first step in applying L'Hôpital's Rule?
Back
Differentiate the numerator and the denominator separately.
7.
FLASHCARD QUESTION
Front
Can L'Hôpital's Rule be applied multiple times?
Back
Yes, if the result after applying the rule is still an indeterminate form, you can apply it again.
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