Please help me check the attached worksheet. I defined the target functions by two ways: factor one parameter delta out in two terms or totally expand them (you can uncomment the definition to play by the remarks). The plots drawn or the evaluation done in the end are quite different. When Maple do maximization or evaluation, what is the difference between these two "algebraic identical" forms?

I was testing if Maple can prove/show limit(a*(1-F(a)), a=infinity,left)=0, where F(.) is a general cumulative distribution function. Though, I doubt Maple has the ability.  However, I come across with some other questions during the exploration:

1. how is maple exactly doing to find limit:
Let's first try a normal distribution case:
 

with(Statistics):
U := RandomVariable(Normal(s,t))  :
limit(CDF(U,x),x=infinity,left)  assuming t>0,t<infinity ;