# Finding the limit of a function

I have the following code:

Ud = (11/10);
Uin = 15*Sqrt[2];
Rb = (15/(2*10^(-3)*(29812/10^3)));
c = (10000*10^(-6) + (22/10)*10^(-6));

y[fin_] = 2*fin*(2*T*Ud - ((Ud)/(fin)) + ((Uin*Sin[2*Pi*fin*T])/(2*Pi*fin))
+ c*Rb*(2*Ud - Uin)*(Exp[-((T)/(c*Rb))] - 1));

Teqn[fin_] = Abs[Uin*Sin[2*Pi*fin*T - (Pi/2)]] - 2*Ud
== (Uin - 2*Ud)*Exp[-T/(c*Rb)];

Tsol[fin_?NumericQ] := FindRoot[Teqn[fin], {T, 1/(4*fin), 1/(2*fin)}];

ListPlot[Table[{fin, y[fin] /. Tsol[fin]}, {fin, 10^(-5), 10000, 10}]]


How can I improve my code so that I can find:

$$\lim_{f_{in}\to\infty}y[fin]=\space\text{?}$$

• Collect[ y[fin] , fin] shows you the structure of your function. There is a linear term O[fin], so the limit doesn't exist! – Ulrich Neumann Aug 1 '18 at 6:56

If I understand the problem correctly, then it is necessary to calculate $y(x,T(x))$ for very large values of $x$. In this case, the code is

Ud = (11/10); Uin =
15*Sqrt[2]; Rb = (15/(2*10^(-3)*(29812/
10^3))); c = (10000*10^(-6) + (22/10)*10^(-6));
y[fin_, T_] :=
2*fin*(2*T*Ud - ((Ud)/(fin)) + ((Uin*Sin[2*Pi*fin*T])/(2*Pi*fin)) +
c*Rb*(2*Ud - Uin)*(Exp[-((T)/(c*Rb))] - 1));
Teqn[fin_] =
Abs[Uin*Sin[2*Pi*fin*T - (Pi/2)]] - 2*Ud == (Uin - 2*Ud)*
Exp[-T/(c*Rb)];
T[fin_] :=
T /. FindRoot[Teqn[fin], {T, 1/(4*fin), 1/(2*fin)}]; LogLogPlot[
y[fin, T[fin]], {fin, 10^-5, 10^10}]