Using L'Hospital's Rule for Indeterminate Form Problems in Calculus

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Homework Help Overview

The discussion revolves around the application of L'Hospital's Rule to evaluate limits that result in indeterminate forms, specifically in the context of calculus problems involving arccosine and logarithmic functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to apply L'Hospital's Rule to two limit problems. Some participants suggest a change of variables to simplify the second limit, while others provide insights into rewriting the function for further analysis.

Discussion Status

Participants are actively engaging with the problems, offering suggestions and clarifications. There is a progression in the discussion as some participants express uncertainty about how to proceed, while others provide guidance on rewriting expressions and applying L'Hospital's Rule.

Contextual Notes

The original poster expresses difficulty in proceeding with the problems, indicating a need for further clarification on the application of the discussed methods. The second limit involves a change of variables that may not be immediately clear to all participants.

blu3jam
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Hi I'm new to this forum, i need a help i don't know how can i use l'hospital in these problems;lim(x->1, ((arccos(x))^lnx))

lim(x->\pi/2+ (cosx ln(x - \pi/2 ) )Can anyone help?
 
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The second one is greatly simplified if you make a change of variables u = x - pi/2
 
nicksauce said:
The second one is greatly simplified if you make a change of variables u = x - pi/2


Thanks, but still i don't know how can i proceed ? =(

lim(u->0+ (cos(u+\pi/2) ln(u ) )
 
Well cos(u+pi/2) = -sin(u)

Then you can write your function as
-ln(u) / csc(u), and then apply l'hopital's rule. See where that gets you.
 
nicksauce said:
Well cos(u+pi/2) = -sin(u)

Then you can write your function as
-ln(u) / csc(u), and then apply l'hopital's rule. See where that gets you.

Now ,i figured it out thank you :wink:
 

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