did this help?1. Find a function that satisfies:
F''(X) = (6/(5*SQRT(x)) + 4
F'(1) = -3
F(4) = -6
integrate F''(x)=(6/(5*sqrt(x))+4 both sides w.r.t x to get F'(x). one arbitrary constant will appear. that constant can be found out by satisfying the equation F'(1)=-3. similarly integrate the expression for F'(x) and hence find F(x).
No idea on this one, I don't remember doing these kinds of problems at all.
Lastly evaluating a limit... I think I'm doing it right but confused. I don't think it's this simple.
I'm evaluating the limit as X approaches E from the right of
((X - LN(X)) \ (LN(X) - 1))
It works out to E - LN(E) in the numerator which is E - 1
and LN(E) - 1 in the denomiator which is 1 -1 = 0
I am left with E-1 / 0 which doesn't seem right to me.