Can L'Hopital's Rule Solve tan(pi*x/2)ln(x) as x Approaches 1?

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Homework Help Overview

The problem involves finding the limit of the expression tan(pi*x/2)ln(x) as x approaches 1, which falls under the subject area of calculus, specifically limits and L'Hôpital's Rule.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of L'Hôpital's Rule and the appropriate form of the limit, with some suggesting rewriting the expression to identify a 0/0 form suitable for differentiation.

Discussion Status

The discussion is ongoing, with participants providing guidance on how to approach the limit using L'Hôpital's Rule. There is a focus on clarifying the correct method of differentiation rather than integration, and multiple interpretations of the problem are being explored.

Contextual Notes

Some participants express confusion regarding the initial approach, particularly the mention of integration, which is not relevant to applying L'Hôpital's Rule in this context.

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Homework Statement


Find the limit as x goes to 1 of tan(pi*x/2)lnx


Homework Equations


using l'hospital's, lim f'(x)/g'(x)=answer


The Attempt at a Solution


i tried integrating by making the tangent part squared so i can divide by the tangent part, but i keep getting stuck. i think the answer is either 1 or infinity.

help please? thanks
 
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I really don't know how you are trying to do the problem. l'Hopital's rule doesn't tell you to integrate anything. Write it as ln(x)/cot(pi*x/2). Now it's a 0/0 form. Now differentiate numerator and denominator like l'Hopital says.
 
woops i meant taking the derivative
 
Integrating has nothing to do with this problem. Try rewriting your limit as
[tex]\lim_{x \to 1}\frac{ln(x)}{cot(x*\pi/2)}[/tex]

Now you have something you can use L'Hopital's Rule on.
 

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