Limit of Function: Find Solution

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SUMMARY

The discussion focuses on solving the limit problem defined as ##\lim_{t\rightarrow 0} \dfrac{\exp(-A/t)}{t^{n/2}}## where A is a positive constant. Participants suggest using variable substitutions, specifically ##u=1/t^{n/2}## and ##u=1/t##, to simplify the expression. The application of L'Hôpital's rule is also mentioned as a potential method for finding the limit. These strategies aim to effectively handle the indeterminate form encountered as t approaches zero.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hôpital's rule
  • Knowledge of exponential functions and their properties
  • Experience with variable substitution techniques in calculus
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  • Study the application of L'Hôpital's rule in depth
  • Explore variable substitution methods for solving limits
  • Investigate the behavior of exponential functions as their arguments approach infinity
  • Practice solving similar limit problems involving exponential decay
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Students studying calculus, particularly those focusing on limits and exponential functions, as well as educators looking for effective teaching strategies in limit evaluation.

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Homework Statement


Find the above limit

Homework Equations


##\lim_{t\rightarrow 0} \dfrac{\exp(-A/t)}{t^{n/2}}## with A>0

The Attempt at a Solution


I tried using the change of variable ##u=1/t^{n/2}##, and then next use LHopital rule, but i don't find the way..
 
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Have you tried taking the natural log of the expression? What about letting u = 1/t rather than the more complex expression?
 

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