computerages Posted January 14, 2007 Share Posted January 14, 2007 Hi everyone, I understand (or should I say "know") the theoretical proof of L'Hopital's rule, but the flipping of equations is not really satisfying my curiosity... my question is that is there any way to picture L'Hopital's rule? by picturing I mean is that we could picture the derivative of a function as h approaching 0 as (x, x-h) gets smaller and smaller, then is there similar or totally different way to picture this rule, or maybe any calculus or even any higher math problem that is only based on equations...? i hope you understood the point of questions, if not please ask me thx! Link to comment Share on other sites More sharing options...
computerages Posted January 17, 2007 Author Share Posted January 17, 2007 it seems like my questions happens to be a weird one.... Link to comment Share on other sites More sharing options...
Ragib Posted January 18, 2007 Share Posted January 18, 2007 Well, heres my best shot. Ok, well the rule applies to composite functions, say f(x)/g(x). When we sub in values we get an indeterminate form. We only want the RATIO of the 2 functions. So say 5x/x, x appraoches zero, 0/0. But since we only want the ratio, we could instead get an approximation that, in the limit, is exact. Our approximation is our tangent line The tangent line has the same value as the point it touches. So basically we found the ratio of the values at the tangents, which is what L'hopitals rule wants. I hope I explained that well... Link to comment Share on other sites More sharing options...
Recommended Posts
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new accountSign in
Already have an account? Sign in here.
Sign In Now