So I need to take the limit of
e*w*L/Sqrt[R^2 + (w*L - 1/(w*C))^2] as w approaches infinity
So in Mathematica it would look like
Limit[e*w*L/Sqrt[R^2 + (w*L - 1/(w*C))^2], w -> Infinity]
All variables are >0
The answer is e, but I am curious as to how to do this. This is not a homework problem as this was something that was partially shown in our physics class and our professor took some serious shortcuts and basically just gave us the answer because he did not want to go through the proof, but I would like to see it.
I understand L'Hopital's rule, but it does not seem to work here as you always have Sqrt[R^2 + (L w - 1/w*C)^2] in your answer no matter how many times you were to take the derivative.
I am wondering if there is another formula to do something like this. If you have any suggestions that would be great.
FYI: e=EMF, w=omega, L= inductance, R=resistance, C=capacitance. This equation is looking for the voltage across the inductor as the frequency approaches infinitely large