I don't know if I've posted this in the right place but I thought I'd give it a go anyway.
Homework Statement
See Attatchment
Homework Equations
The Attempt at a Solution
So for part a) max z:150X11+350X12+300X13+100X21+500X22+400X23
s.t. X11+X12+X13≤40...
Homework Statement
Use Taylor's theorem to estimate |(ex)-x-1| for 0≤x≤1. Thus prove that if a>(1/2) then:
f(x)=(1-|x|a)*(ex)a is differentiable at x=0
Homework Equations
The Attempt at a Solution
So |(ex)-x-1|=(x^2)/2+(x^3)/6+(x^4)/24...
But I don't see how this helps, I...
Sorry just realized the bottom part of the limit is wrong as after you've differentiated once your going to have to use the product rule after that. Could you just use induction on the degree m then, and then use L'hopitals rule to prove it for n+1?
Oh ok, didn't think of using l'Hopitals rule. So can you just say:
Lim_{y->Inf} Q(y)/ey2 <=> lim_{y->inf} Q(m)(y)/((2y)m).ey2)
<=> Lim_{y->inf} a(m).m!/((2y)m).ey2)=0
Is that right?
Homework Statement
Q(y)=a0+a1y+...+amy^m is a polynomial of degree m and I need to show that:
Lim{y->Inf} Q(y)/ey2=0
Homework Equations
The Attempt at a Solution
It seems obvious but I can't seem to be able to prove it, and don't really know where to start, any help...