So I've come across this formula that I derived. y(t) =v(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}t/√(v^{2}t^{2}+b^{2})

I would like to solve the limit of t to infinity analytically. When I apply L'Hopital I get

y = lim v^{2}/ lim v^{2}t/√(v^{2}t^{2}+b^{2})

but as you can see I would have to apply L'Hopital rule an infinite amount of times, now I don't know if you say it becomes x/(x/(x/..))). with x= v^{2}whatever value that is.

By inspection of a grapher I would say it's v , it also looks like v*sin(arctan(v/b*t)), which at t-> arctan -> pi/2 then sin() -> 1 so the answer is v. But, how do I know arctan(t) t->inf it pi/2 besides geometrically it makes sense.

Any ideas about the infinite L'Hopital, or infinite divisions how something like that could be solved.

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# L'Hopital ad infinitum

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