L'hopital's Rule for solving limit problem

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Homework Help Overview

The discussion revolves around evaluating the limit of the expression (x-1)^3/log(x) as x approaches 1, specifically using L'Hôpital's Rule. Participants are exploring the conditions under which L'Hôpital's Rule can be applied.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply L'Hôpital's Rule by differentiating the numerator and denominator but expresses uncertainty about the correctness of their approach. Other participants question the conditions for using L'Hôpital's Rule, particularly regarding the limits approaching zero.

Discussion Status

The discussion is active, with participants providing differing views on the application of L'Hôpital's Rule. Some guidance has been offered regarding the necessary conditions for the rule, but there is no explicit consensus on the best approach to take.

Contextual Notes

There is a mention of the need for both the numerator and denominator to approach zero or infinity, which is a point of clarification in the discussion.

kmeado07
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The question is:
Evaluate the following limit: lim(as x tends to 1) of [(x-1)^3]/(logx)

I tried using L'hopital's Rule, so i differentiated the top and bottom of the eqn and i got 3x(x-1)^2, then as x tends to 1 this would tend to 0.

I don't think this is correct though, and was wondering if anyone could give me some guide lines to maybe another rule to use to find the limit.

Thanks.
 
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kmeado07 said:
I don't think this is correct though, and was wondering if anyone could give me some guide lines to maybe another rule to use to find the limit.
Why would you think so? It's perfectly correct, well done.
 


But to use l'hopital's rule, don't you need the limit, x, tending to zero?
 


No, you only need both the numerator and the denumerator tend to zero (or infinity) as x approaches some number a, for example one.
 

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