Video Game Forums - View Single Post - Don't often do this, but ARGH at this math problem

***CaptHayfever*** · 04-23-2007, 12:07 PM

Thank you, Ace!

The limit does not exist. Whether it tends towards upper or lower infinity or not, I can't be certain at this point, though I would presume neither.

Why:
Finding limits this intricate, unless your teacher is a sadist who makes you do epsilon-delta proofs for each one, just involves evaluating at the value x approaches, in this case x->0. Having the cubed x in the denominator, though, is not a guaranteed infinite limit, as it might divide out or L'Hospital's rule might be applied. This is why I couldn't answer before solving the obscure integral form.
We can now see that the cubed x does NOT divide out, nor does the "numerator" evaluate to 0, so L'Hospital is out of the question. Our fate is sealed; there is no limit.
I'm inclined towards a full-blown DNE instead of +-infinity because of the logarithms. Put 0 into that first log term, and you're staring at log(-1), which is utterly preposterous, whether the base is 10 or e.

And remember, "I'm-a Luigi, number one!"

04-23-2007, 12:07 PM	#12
*CaptHayfever* Smash Supermod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 20,350 Thanks: 400 Thanked 1,141 Times in 668 Posts Points: 130,495.10 Bank: 4,160.91 Total Points: 134,656.02 Donate	Thank you, Ace! The limit does not exist. Whether it tends towards upper or lower infinity or not, I can't be certain at this point, though I would presume neither. Why: Finding limits this intricate, unless your teacher is a sadist who makes you do epsilon-delta proofs for each one, just involves evaluating at the value x approaches, in this case x->0. Having the cubed x in the denominator, though, is not a guaranteed infinite limit, as it might divide out or L'Hospital's rule might be applied. This is why I couldn't answer before solving the obscure integral form. We can now see that the cubed x does NOT divide out, nor does the "numerator" evaluate to 0, so L'Hospital is out of the question. Our fate is sealed; there is no limit. I'm inclined towards a full-blown DNE instead of +-infinity because of the logarithms. Put 0 into that first log term, and you're staring at log(-1), which is utterly preposterous, whether the base is 10 or e. And remember, "I'm-a Luigi, number one!"