Does exponential take over cosine?

[EvLer]

If i have a response for a circuit that consists of: cos(t) + e^-t + e^3tand if I let t->infinity, does exponential "over-take" cos(t)?
well, the actual question is whether the output/response remains finite as t->infinity...

thanks, as always

 

[Warr]

maybe I'm misunderstanding you but...
lim t-> infinity cos(t) + e^-t + e^3t = infinity

 

[HallsofIvy]

You are aware, are you not, that cos(x) is never larger than 1? It doesn't take much for any function to "overtake" (which is not the same as "take over"!) cos(x).