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Wed 10 Nov, 2004 12:49 am
I am introducing myself, good lookin female -- double major for BS in physics and BA in technical theatre with math minor -- freaking out over calculus ineptitude and jealous of the only 2 people in my class who actually "get it". check out my webpage if you want to get to know me Edit (Moderator): Link removed I Just need some reasurance or correction for two problems that use L'hospital's Rule.
1. The lim as x->infinity of (1 + a/x) to the power bx.
I managed to get lim of (a(bsquared))/ (1 +a/x) = + infinity with some implicit differentiation and I could be totally wrong but at some point I need to get the right answer into the form e but I am having a brain cramp or something and I can't find it anywhere I was thinking the answer was e to the x power but I have a feeling it can't be that easy and there are more terms floating around that need to be included in the e form.
2. So when proving this: The lim as x-> infinity for (lnx)/(x to the power p) = 0
It is because when we use L'hospital's rule we get eventually lim (1/x)/(P!)
Right? but where do I go from here to get to prove that for any p>0 that the logarithmic function approaches infinity more slowly than any power of x. Do I need to do L'hospital's again and if I do what is the logarithmic form I'm supposed to sub in to get back into a form where the lim of the function is determinate one and is zero?
Butterfryby - yours is the sloppiest description of a mathematical problem I've ever had the misfortune to see. You'll get exactly nowhere until and unless you discipline yourself to write symbols correctly, e.g. "to the power of" as "^" (with a basic keyboard, which lacks subscripts and exponents) and ever words correctly - like the mathematician's name.
I doubt you'll figure out the problem even after the above corrections, though, so here's an analogous problem complete with its solution >>
http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-01Fall2003/14C1BBCC-7F4C-41AA-81DC-1E6D9D57022D/0/pracsolns.pdf
>> assuming optimistically you know how to get to the second page of the linked text and look up problem 4. Good luck - miracles happen, you need one. Alternatively you could stick to the "technical theater" in which you may be talented for all I know.
HofT wrote:Butterfryby - yours is the sloppiest description of a mathematical problem I've ever had the misfortune to see. You'll get exactly nowhere until and unless you discipline yourself to write symbols correctly, e.g. "to the power of" as "^" (with a basic keyboard, which lacks subscripts and exponents) and ever words correctly - like the mathematician's name.
I doubt you'll figure out the problem even after the above corrections, though, so here's an analogous problem complete with its solution >>
http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-01Fall2003/14C1BBCC-7F4C-41AA-81DC-1E6D9D57022D/0/pracsolns.pdf
>> assuming optimistically you know how to get to the second page of the linked text and look up problem 4. Good luck - miracles happen, you need one. Alternatively you could stick to the "technical theater" in which you may be talented for all I know.
That may be the rudest post I've ever had the misfortune to read. I hope the gods of A2K strike you down.
Butterfryby, please ignore HofT as she apparently has a vat of boiling bile inside her and so everything comes out like that.
The quickest way to solve the limit problems is to break them up. Then think of them as a race to see who gets to infinity faster. Example:
lim x-> infinity of (1 + a/x )^bx. Since it is x that is moving to infinity, look at the terms containing x, starting inside the brackets. a/x goes to zero as x goes to infinity, so you have left (1)^bx. 1 raised to any power is 1, so the answer should be 1, unless I misread the problem.
For number 2, I believe you need LH, since it is of the form infinity/infinity ( it think, can't remember which way ln goes wrt x) so you have to take the derivative of the top and the bottom. You should get (1/x)/(px^p-1) which reduces to 1/px^p which goes to zero.
This problem involves the definition of e (base of natural log system) and if you don't recognize it, it is very hard to solve. If you let Y=X/A, this problem simplifies to [(1+1/Y)^Y]^AB as Y->infinity. The section inside the brackets is the definition of e, so the answer is e^AB.
I'm not sure you can solve this using LH's principle. You end up with a series of the form 1+1/1!+1/2!+1/3!... which is also a definition of e.
Engineer - since you read the other thread you know that the original poster solved the problem, so further discussion is moot. You're right about the asymptotic limit btw but that's simply a solution by analogy as in the examples given in the link I posted above.
MerlinsGodson wrote:HofT wrote:Butterfryby - yours is the sloppiest description of a mathematical problem I've ever had the misfortune to see. You'll get exactly nowhere until and unless you discipline yourself to write symbols correctly, e.g. "to the power of" as "^" (with a basic keyboard, which lacks subscripts and exponents) and ever words correctly - like the mathematician's name.
I doubt you'll figure out the problem even after the above corrections, though, so here's an analogous problem complete with its solution >>
http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-01Fall2003/14C1BBCC-7F4C-41AA-81DC-1E6D9D57022D/0/pracsolns.pdf
>> assuming optimistically you know how to get to the second page of the linked text and look up problem 4. Good luck - miracles happen, you need one. Alternatively you could stick to the "technical theater" in which you may be talented for all I know.
That may be the rudest post I've ever had the misfortune to read. I hope the gods of A2K strike you down.
Now the debate must begin whether or not to strike down a rude post along with a valuable resource.
I thiught it was pretty good.
I see the conundrum.
Let's just say there is a limit to rude posts. (bowling for dollars...)
(I see I am speaking up here, unusual. Often swattable posts. Still, I listen. Watching this one.)
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