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wu :: forums    riddles    putnam exam (pure math) (Moderators: Grimbal, Eigenray, SMQ, towr, william wu, Icarus)    lim x->inf (x^t/e^x)=0 « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: lim x->inf (x^t/e^x)=0  (Read 1112 times) svs14 Newbie     Posts: 8 lim x->inf (x^t/e^x)=0   « on: Sep 17th, 2004, 10:47pm » Quote Modify hey can someone help me out with this lim x->inf (x^t/e^x)=0 for any real number, t. how do i prove this. thanks IP Logged Benoit_Mandelbrot Junior Member Almost doesn't count.     Gender: Posts: 133 Re: lim x->inf (x^t/e^x)=0   « Reply #1 on: Sep 17th, 2004, 10:51pm » Quote Modify Through the Principle of Induction, I believe.  How would you do it with that? « Last Edit: Sep 17th, 2004, 10:53pm by Benoit_Mandelbrot » IP Logged Because of modulo, different bases, and significant digits, all numbers equal each other! svs14 Newbie     Posts: 8 Re: lim x->inf (x^t/e^x)=0   « Reply #2 on: Sep 17th, 2004, 10:53pm » Quote Modify oh yeah...through the principle of induction... this question follows after another one which is exactly the same but t>=0 in the earlier one. if that helps IP Logged william wu wu::riddles Administrator     Gender: Posts: 1291 Re: lim x->inf (x^t/e^x)=0   « Reply #3 on: Sep 18th, 2004, 2:20am » Quote Modify When t=0, your function is e^(-x), which clearly goes to 0. When t<0, your function is x^(-t)e^(-x), which also clearly goes to 0. And the > 0 case is handled by the previous problem. In that case, I think you can invoke L'Hospital's rule and repeatedly differentiate numerator and denominator. The denominator is always e^x, but in the numerator eventually all positive powers of x are whittled off, and so you reduce to the (t <= 0) cases. IP Logged [ wu ] : http://wuriddles.com / http://forums.wuriddles.com Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7526 Re: lim x->inf (x^t/e^x)=0   « Reply #4 on: Sep 18th, 2004, 11:31am » Quote Modify Why not write:  x^t/e^x = e^(t ln x - x).  It obviously goes to 0.  No? « Last Edit: Sep 18th, 2004, 11:32am by Grimbal » IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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