Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20121028 21:49:01
Why can't I use L'Hopital here?To evaluate why can't I just use L'Hopital's rule? I was told that I couldn't because it's a circular proof, but I don't understand why... I know you evaluate this using the squeeze theorem (to show that it's 1) but L'Hopital's rule seems a lot easier to use here. #2 20121028 22:11:14
Re: Why can't I use L'Hopital here?It is because the derivative of the sine function is found through that limit. Evaluating it using something that ot proves is a circular proof. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20121028 22:25:22
Re: Why can't I use L'Hopital here?Oh of course, I see. So it follows that I can't use the one for cosine either (I think that's used in the proof of derivative of sine). Thanks. #4 20121028 22:55:20
Re: Why can't I use L'Hopital here?That is right. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #5 20121028 23:03:10
Re: Why can't I use L'Hopital here?Hi zetafunc;; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20121028 23:29:09
Re: Why can't I use L'Hopital here?hi You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20121028 23:32:02
Re: Why can't I use L'Hopital here?I cannot see on any of those websites an explanation of why they are able to use L'Hopital's rule for sinx/x. They have used it but have not justified their use of it. #8 20121028 23:38:55
Re: Why can't I use L'Hopital here?Hi;
Not just sites but published PDF's, MIT lecture on youtube, and textbooks! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121029 01:00:44
Re: Why can't I use L'Hopital here?Thanks for finding another way to establish the derivative of sin. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20121029 01:12:41
Re: Why can't I use L'Hopital here?He seems to be using x as the angle of the sector and as the distance along the horizontal axis ?? You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #11 20121029 03:45:02
Re: Why can't I use L'Hopital here?Why can't you just use the definition of sine and differentiate that? #12 20121029 03:46:14
Re: Why can't I use L'Hopital here?And, surely you can just prove that cosine is the derivative of sine by differentiating the definition of sine and showing that it's equal to the definition of cosine...? #13 20121029 03:49:50
Re: Why can't I use L'Hopital here?
Thatis not the definition of sine. That is a result derivable from Euler's theorem. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #14 20121029 05:40:56
Re: Why can't I use L'Hopital here?Does that invalidate the method? You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #15 20121029 11:23:42
Re: Why can't I use L'Hopital here?Hi Bob and Zetafunc; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 