need to demmonstrate l'hopital rule using examples of 0/0, infinity/infinity, 0/infinity and infinity/0....help?

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need to demmonstrate l'hopital rule using examples of 0/0, infinity/infinity, 0/infinity and infinity/0....help?

Mathematics
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that is easy, but l'hopital rule only apply for 0/0 and infinity/infinity
ln(x)/x
for inf/inf

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Other answers:

0/infinity always give 0 and infinity/0 always get infinity
l'hopital only aply to o/o infinty/infinity here o/infinity = o & infinity/o= infinity
xln(x/(x-1)) for 0/0
one example is lim as n--> 0 of sin(x)/x in this case you would use l'hopitals rule to derivve sin(x) and x so derivative if sin(x) = cos(x) and x --> 1. so now you hvae lim as n approaches 0 of cos(x) which is 1. so your answe rfor limit as n approaches 0 for sin(x)/x = 1
(x^2 - 1)/(x-1) as x --> 1, this is a simple 0/0
what is the answer supposed to be for them though, like is it a set answer or can they be different cause i've seen example that give like 7/13 and i'm just like :S
i have to explain it, so gonna site this website then give examples fr all four showing only 2 work i'm guessing ;/

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