Does exponential take over cosine?

AI Thread Summary
As t approaches infinity in the circuit response of cos(t) + e^(-t) + e^(3t), the exponential term e^(3t) dominates the behavior of the function. The limit of the entire expression tends to infinity due to the rapid growth of e^(3t), while cos(t) remains bounded between -1 and 1. The exponential terms e^(-t) and e^(3t) significantly influence the output, with e^(3t) being the primary contributor to the overall response. Thus, the output does not remain finite as t approaches infinity. The discussion clarifies that exponential functions can indeed "overtake" cosine in terms of growth.
EvLer
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If i have a response for a circuit that consists of: cos(t) + e-t + e3tand 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 :smile:
 
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maybe I'm misunderstanding you but...
lim t-> infinity cos(t) + e^-t + e^3t = infinity
 
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).
 

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