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1.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even. 2.Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2. 3.let r>0 and S={x in R^3:(x1)^2+(x2)^2+(x3)^2<(r)^2} show that diam S=2r.4.let x=(x1,...xn) in Rn.show that (? k=1,n xk)^2<=n|x|^2.
Prove that the Digraph of a partial order has no cycle of length greater than 1. Assume that there exists a cycle of length n ≥ 2 in the digraph of a partial order ≤ on a set A
Symmetry Definition : A line of symmetry divides a set of points into two halves, each being a reflection of the other. Each image point is also a point of the set. Defin
Derivatives of Hyperbolic Functions : The last set of functions which we're going to be looking at is the hyperbolic functions. In several physical situations combinations of e
Curvature - Three Dimensional Space In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require → r′ (t) is continuou
Maxima and Minima We have to make a distinction between relative maxima (or minima) and global maxima (or minima). Let f(x) be a function of x. Then the global maxi
theory about solving sequencing problem using graphical method
At time t an investor shorts a $1 face value zero coupon bond that matures at time T = t and uses the entire proceeds to purchase a zero coupon bond that matures at time
write in factor form 9x3+9x5
Explain Lobachevskian Geometry and Riemannian Geometry ? Nineteenth century mathematician Nicolai Lobachevsky assumed that the summit angles of a Saccheri quadrilateral are ac
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
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