- #1
Turion
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Homework Statement
Homework Equations
The Attempt at a Solution
Are you allowed to do that where you just apply L'H an infinite amount of times?
Solving a limit with L'H's rule
- Thread starter Turion
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In summary, L'Hôpital's rule is a mathematical technique used to evaluate limits of functions with indeterminate forms. It should only be applied when other methods have failed, and involves taking the derivative of the function and evaluating the limit with the new derivatives. However, there are limitations to its use, as it can only be applied to certain types of functions and limits. It is not a universal solution and other methods may be needed for different types of limits.
Are you allowed to do that where you just apply L'H an infinite amount of times?
- #2
Mark44
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Turion said:Homework Statement
Homework Equations
The Attempt at a Solution
After taking the derivative of the denominator, you should get et, not eα. I suspect that was a typo.
Anyway, your limit is correct. The basic idea is that power functions, such as tα grow large, but exponential functions grow large faster.
1. What is L'Hôpital's rule?
L'Hôpital's rule is a mathematical technique used to evaluate the limit of a function that has an indeterminate form, such as 0/0 or ∞/∞. It can be used to simplify complex limits and make them easier to solve.
2. When should L'Hôpital's rule be applied?
L'Hôpital's rule should only be applied when the function is in an indeterminate form and the limit is not immediately obvious. It should also be used when other methods, such as factoring or substitution, have failed to solve the limit.
3. How do I use L'Hôpital's rule?
To use L'Hôpital's rule, take the derivative of both the numerator and denominator of the function separately. Then, evaluate the limit using these new derivatives. If the limit is still in an indeterminate form, repeat the process until a solution is reached.
4. Are there any limitations to using L'Hôpital's rule?
Yes, there are some limitations to using L'Hôpital's rule. It can only be used on functions that are continuous and differentiable in the given interval. It also cannot be used on limits that involve discrete values, such as integers, or limits that approach a vertical asymptote.
5. Can L'Hôpital's rule be used to solve all limits?
No, L'Hôpital's rule cannot be used to solve all limits. It is only applicable to limits that have an indeterminate form. There are many other methods and techniques that can be used to solve limits, depending on the specific function and limit in question.
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