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Calculating the limits

  • Thread starter ada0713
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  • #1
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Homework Statement



lim[p[tex]\rightarrow[/tex]0] [tex]\frac{ ln(2x^{p}+3y^{p})}{p^2}[/tex]

Homework Statement




I first plugged in zero to see if i can you L'hopital's rule
I got a (constant)/0 which is not an indeterminant form.

If I can't use the rule, what should be my next step to find the limit?
( I kinda guessed that the the answer's infinity but I'm not sure)
 

Answers and Replies

  • #2
You don't need L'hopital's rule here since the numerator is always constant... The answer is more straight forward than you think...

What's lim [x->infinity] 1/(x^2) ?

edit: didn't notice that x was to the power of p...see office shredder's comment
 
Last edited:
  • #3
Office_Shredder
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The numerator isn't constant, but it approaches one...
also, the limit is as p goes to 0, not infinity.

I suspect the easiest way to be rigorous is to bound ln(...) from above and below for small enough p, which gives you that constant/0 term. It's not always infinity though... you haev to be careful of the existence and sign of ln(...) depending on what values x and y take (note they have to be non-negative, or the limit definitely doesn't exist, for example)
 

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