- #1
stunner5000pt
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Show for every real x, that [tex] f(x) = \lim_{n \rightarrow \infty} ( \lim_{m \rightarrow \infty} (cos n! \pi x)^{2m}) [/tex] exists and compute it. (show as a familiar rational number) Provein deatil taht your calculations are correct.What is a more familiar name for the function f?
The argument of the Cosine is a real number, and since the cosine fuctin maps from Reals to Reals then the cosine part exists and is real. But how owuldi deal with the limit parts? L'Hopital's rule doesn't apply here...
Doesnt the cosine function wave up and down?? So hgow would this limit exist then?
ANy help would be greatly appreciated! Thanks!
The argument of the Cosine is a real number, and since the cosine fuctin maps from Reals to Reals then the cosine part exists and is real. But how owuldi deal with the limit parts? L'Hopital's rule doesn't apply here...
Doesnt the cosine function wave up and down?? So hgow would this limit exist then?
ANy help would be greatly appreciated! Thanks!