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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.
A man travels 600km partly by train and partly by truck. If he covers 120km by train and the rest by truck, it takes him eight hours. But, if he travels 200km by train and the res
"Standard" trig equation: Now we need to move into a distinct type of trig equation. All of the trig equations solved to this point were, in some way, more or less the "standard"
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
Find the equation for each of the two planes that just touch the sphere (x - 1) 2 + (y - 4) 2 + (z - 2)2 = 36 and are parallel to the yz-plane. And give the points on the sphere
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
cos inver
Find the circumference of a circle whose area is 16 times the area of the circle with diameter 7cm (Ans: 88cm) Ans: Π R 2 = 16 Π r 2 R 2 = 16 r 2
50387 divided by 21
Prove that the Poset has a unique least element Prove that if (A, ) has a least element, then (A,≤) has a unique least element. Ans: Let (A, ≤) be a poset. Suppose the po
One box can hold 5 1/2 lbs of nuts and 3 lb 6oz of bolts. What is the total weight for one box?
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