Table of contents |
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What is L'Hôpital's Rule? |
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Applying L'Hôpital's Rule: A Step-by-Step Example |
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Practice Problems for L'Hôpital's Rule |
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Solutions to Practice Problems |
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Conclusion |
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From earlier studies, you might remember that certain limits of functions result in indeterminate forms like 0/0 or ±∞/∞. These forms are ambiguous and cannot be evaluated directly. Instead of manipulating the expression algebraically to resolve the indeterminacy, we can use a powerful tool called L'Hôpital's Rule, which leverages derivatives to simplify the process.
Basically, the rule states that we can evaluate the limits of indeterminate forms using their derivatives!
This means you can find the limit by taking the derivatives of the numerator and denominator separately and then evaluating the new limit. Note that L'Hôpital's Rule is distinct from the quotient rule for derivatives and is only applicable to these specific indeterminate limit cases.
This is an indeterminate form, so L'Hôpital's Rule is appropriate. First, verify the conditions by checking the limits of the numerator and denominator:
Since L’Hopital’s Rule can be applied. Be sure to write this statement out before actually applying this rule.
Now, we can take the derivatives and get into L’Hopital’s Rule.
In conclusion, we know that this limit…
Question 2 Solution
Plugging x = ∞ into results in the indeterminate form
Therefore, we should use L’Hopital’s Rule.
Since L’Hopital’s Rule can be applied.
Key Terms to Understand
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1. What is L'Hôpital's Rule and when can it be applied? | ![]() |
2. How do you apply L'Hôpital's Rule step-by-step? | ![]() |
3. Can L'Hôpital's Rule be applied more than once? | ![]() |
4. What are some common indeterminate forms that L'Hôpital's Rule can be used for? | ![]() |
5. Are there any limitations or conditions for using L'Hôpital's Rule? | ![]() |