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!

it seems like my questions happens to be a weird one....

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...