Limit Approach to infinity

syms I(t) N Mu Gamma Vo V(t) %Used to decalre variables as symbol

I(t) = Io*exp(-Mu*t);

ode = diff(V,t) == Mu.*N.*I(t) - Gamma.*V(t); %Equation Writing

cond = V(0) == Vo; %Initial condition

Solution_eq3 = dsolve(ode, cond) %Solution the the modified equation == Solution to the IVP

%------------------------------------------------------------------------------------------------------

%PART -----> (c)

Solution = log(Solution_eq3)

Limits = limit(Solution,t,Inf)

Limit not approaching to infinity.

Answer 1

[Harshitha Kallam]

Hi Fahad,

When using syms, you should break it down into symbols that are certain to be real valued and those that are not certain, and you should add the "real" qualifier when possible. For example,

syms Io Vo N real 
syms Gamma   %potentially complex valued 

You should also add any assume calls that are reasonable. For example,

assume(Io >= 0) 

With all of your symbols being potentially complex valued (because you did not say otherwise), and in case any of your values might be 0, MATLAB is unable to determine the complex sign of the expression. Hence, it gives the output in general about limits, with it not being able to prove anything about the properties of that limit.

So, make sure that you add all the reasonable assumptions so that MATLAB will be able to accurately determine the sign of the expression thereby giving an accurate result for the limit.

Please refer to documentation for the use of assume call.