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Turion
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Homework Statement
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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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SUMMARY
The discussion centers on applying L'Hôpital's rule to solve limits involving exponential and power functions. Participants confirm that it is permissible to apply L'Hôpital's rule multiple times until a determinate form is achieved. A key point raised is the differentiation of the denominator, where the correct derivative is noted as et instead of eα, indicating a potential typo. The consensus is that exponential functions outpace power functions in growth, which is crucial for evaluating limits.
PREREQUISITES- Understanding of L'Hôpital's rule
- Knowledge of derivatives and differentiation techniques
- Familiarity with limits in calculus
- Concept of growth rates of functions, particularly exponential vs. polynomial
- Study advanced applications of L'Hôpital's rule in calculus
- Explore the properties of exponential functions compared to polynomial functions
- Learn about Taylor series expansions for approximating functions
- Investigate common limit forms and their resolutions in calculus
Students studying calculus, particularly those tackling limits and derivatives, as well as educators looking for examples of L'Hôpital's rule applications.
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.
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