L'hopital's Rule for solving limit problem

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The discussion revolves around evaluating the limit of [(x-1)^3]/(logx) as x approaches 1 using L'Hôpital's Rule. The original poster attempted to differentiate the numerator and denominator but expressed uncertainty about the correctness of their approach. Participants clarified that L'Hôpital's Rule is applicable when both the numerator and denominator approach zero or infinity, not just when x approaches zero. The conversation emphasizes the proper conditions for applying L'Hôpital's Rule and reassures that the initial differentiation was indeed correct. Overall, the thread provides guidance on using L'Hôpital's Rule effectively for limit problems.
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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