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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 number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9. What is the probability that the product xy of the two
what is equizilent to 2/5
Scatter Graphs - A scatter graph is a graph that comprises of points which have been plotted but are not joined through line segments - The pattern of the points will defin
We now focus on the use of Datalog for defining properties and queries m graphs. (a) Suppose that P is some property of graphs definable in Datalog. Show drat P is preserved und
Definite Integral : Given a function f ( x ) which is continuous on the interval [a,b] we divide the interval in n subintervals of equivalent width, Δx , and from each interval se
Magnitude - Vector The magnitude, or length, of the vector v → = (a1, a2, a3) is given by, ||v → || = √(a 1 2 + a 2 2 + a 2 3 ) Example of Magnitude Illus
Lines- Common Polar Coordinate Graphs A few lines have quite simple equations in polar coordinates. 1. θ = β We are able to see that this is a line by converting to Car
The sum of two numbers is 19, their difference is 5. find the numbers
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Solving for X in isosceles triangles
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