sin-3x/sin4x as x approaches 0, impossible? i think so, prove me wrong
Name:
Anonymous2007-09-30 21:56 ID:Tyku7148
-3/4.
L'Hopital's rule is the easy way, provided you know it/are allowed to use it.
The hard way: Prove L'Hopital's rule.
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Anonymous2007-10-01 11:13 ID:Kiyn8PyE
L'Hopital's rule is proven by something called the sandwich rule i think, by using that it can be easily proofed that lim ((sinx)/x) when x approaches 0 is 1.
Name:
Anonymous2007-10-01 16:33 ID:I8NAwmH2
lim f(x)/g(x) = lim f'(x)/g'(x)
x-> c x-> c
l'hôpita's rule for indeterminative forms (0/0, infinity/infinity)
Name:
Anonymous2007-10-02 1:04 ID:Ud3mCKKQ
>>3
L'Hopital's rule is proven by algebraic manipulation of the definition of the derivative.
Name:
Anonymous2007-10-02 11:19 ID:UiIt2V+H
Actually, you can only prove L'Hopital's rule through algebra if you cheat and assume things that may or may not hold.
A general proof for all possible limit values is actually very complex.