I use the command Limit,
In[503]:= eq1 =
cinf/(s - \[Theta]c) + (
Sqrt[Dc] E^((lh Sqrt[s])/Sqrt[Dc] - (Sqrt[s] x)/Sqrt[Dc]) F1)/(
Sqrt[s] (s - \[Theta]c)) - (cinf \[Theta]c)/(s (s - \[Theta]c)) + (
E^((Sqrt[s] x)/Sqrt[Dc]) s a[1][s])/(s - \[Theta]c) + (
E^((2 lh Sqrt[s])/Sqrt[Dc] - (Sqrt[s] x)/Sqrt[Dc]) s a[1][s])/(
s - \[Theta]c) - (E^((Sqrt[s] x)/Sqrt[Dc]) \[Theta]c a[1][s])/(
s - \[Theta]c) - (
E^((2 lh Sqrt[s])/Sqrt[Dc] - (Sqrt[s] x)/Sqrt[Dc]) \[Theta]c a[1][
s])/(s - \[Theta]c)
Out[503]= cinf/(s - \[Theta]c) + (
Sqrt[Dc] E^((lh Sqrt[s])/Sqrt[Dc] - (Sqrt[s] x)/Sqrt[Dc]) F1)/(
Sqrt[s] (s - \[Theta]c)) - (cinf \[Theta]c)/(s (s - \[Theta]c)) + (
E^((Sqrt[s] x)/Sqrt[Dc]) s a[1][s])/(s - \[Theta]c) + (
E^((2 lh Sqrt[s])/Sqrt[Dc] - (Sqrt[s] x)/Sqrt[Dc]) s a[1][s])/(
s - \[Theta]c) - (E^((Sqrt[s] x)/Sqrt[Dc]) \[Theta]c a[1][s])/(
s - \[Theta]c) - (
E^((2 lh Sqrt[s])/Sqrt[Dc] - (Sqrt[s] x)/Sqrt[Dc]) \[Theta]c a[1][
s])/(s - \[Theta]c)
In[504]:= eq2 = (Limit[Expand@eq23, x -> + \[Infinity],
Assumptions -> {s > 0, Dc > 0}]) // Simplify // Normal
Out[504]= \[Infinity] a[1][s]
Please tell me where they are,
cinf/(s - \[Theta]c)-((cinf \[Theta]c)/(s (s - \[Theta]c)))