How Do You Find the Limit When L'Hopital's Rule Fails?

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    L'hopital's rule
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SUMMARY

The discussion centers on finding the limit as x approaches infinity for the expression [(9x + 1) ^ (1/2)] / [(x + 1) ^ (1/2)]. L'Hopital's Rule is explicitly noted as ineffective for this problem due to the function cycling. The correct limit is established as 3, confirming the solution provided in the initial guidance.

PREREQUISITES
  • Understanding of limits in calculus
  • Familiarity with L'Hopital's Rule
  • Knowledge of algebraic manipulation of expressions
  • Experience with evaluating limits at infinity
NEXT STEPS
  • Study the application of L'Hopital's Rule in various scenarios
  • Explore alternative methods for finding limits, such as algebraic simplification
  • Learn about the behavior of functions as they approach infinity
  • Investigate the concept of indeterminate forms in calculus
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Students and educators in calculus, mathematicians exploring limits, and anyone seeking to deepen their understanding of L'Hopital's Rule and limit evaluation techniques.

niyati
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I'm suppose to find the limit as x goes to infinity of [(9x + 1) ^ (1/2)] / [(x+1) ^ (1/2)].

L'Hopital's Rule does not work on here (it said so even in the directions) as the function keeps on cycling.

...they gave us the answer (3) but I need to find out how.

:S
 
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Nevermind.

Figured it out.

:DDD
 

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