miguel lopez <miguel39123 <at> hotmail.com> writes:
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> A new rule is necessary:
Tracing:
limit(sin(sin(sin(x)^1000)^4)/x^4000,x,0):
try
sin(sin(sin(x)^1000)^4 = sin(sin(x)^1000)^4 = (sin(x)^1000)^4 = (x^1000)^4
= x^4000
know you see limit x^4000 = 0 so this is correct: sin(sin...) equivalent x^4000
then:
limit(x^4000/x^4000,x,0) = 1, o.k.
4 recursions (not very much).
Recall: sin(u) = u (equivalency of infinitesimals).
exp(u) -1 = u, etc...
I know that you know, but anyway, if someone care, recall: f equivalent to g
when lim f/g = 1
Best wishes
-M