Am I allowed to use L'Hopitals rule?

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SUMMARY

The discussion centers on the application of L'Hôpital's Rule to evaluate the limit \(\lim_{n→∞} \frac{\sin(\frac{1}{\sqrt{n}})}{\frac{1}{\sqrt{n}}}\). Participants clarify that L'Hôpital's Rule can be applied when both the numerator and denominator approach 0 or ±∞. In this case, as \(n\) approaches infinity, both the numerator and denominator approach 0, confirming that L'Hôpital's Rule is applicable for this limit evaluation.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hôpital's Rule
  • Knowledge of trigonometric functions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Review the conditions for applying L'Hôpital's Rule
  • Practice evaluating limits using L'Hôpital's Rule with various functions
  • Explore the concept of indeterminate forms in calculus
  • Study the behavior of trigonometric functions as their arguments approach 0
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Students studying calculus, particularly those learning about limits and L'Hôpital's Rule, as well as educators looking for examples to illustrate these concepts.

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Homework Statement


Evaluate \lim_{n→∞} \frac{sin(\frac{1}{\sqrt{n}})}{\frac{1}{\sqrt{n}}}

Homework Equations





The Attempt at a Solution


Can I use L'Hopital's rule? If not, any ideas?

BiP
 
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When can you use the hospital rule in general? Is this problem of that form? You need to be able to figure that out on your own.
 

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