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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.
Binomial Distribution Consider a batch of N light bulbs. Each bulb may be defective (S) or non-defective (F). The experiment involves selecting a light bulb and checking whethe
12.+12+
A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.
Three-person Problem of Points: Pascal, Fermat and their old friend the Chevalier de Mere each put $10.00 into a pot, and agree to play a game that has rounds. Each player has the
Relationship between the inverse sine function and the sine function We have the given relationship among the inverse sine function and the sine function.
Ray cut 6 pieces of rope . Each piece was between 67 and 84 inches long. What would be the total length of the 6 pieces of rope?
L.H.S. =cos 12+cos 60+cos 84 =cos 12+(cos 84+cos 60) =cos 12+2.cos 72 . cos 12 =(1+2sin 18)cos 12 =(1+2.(√5 -1)/4)cos 12 =(1+.(√5 -1)/2)cos 12 =(√5 +1)/2.cos 12 R.H.S =c
What is a truth table? Distinguish between Tautology & Contradiction?
A garden in the shape of a rectangle is surrounded through a walkway of uniform width. The dimensions of the garden only are 35 by 24. The field of the garden and the walkway toget
For a population with a mean of μ=70 and a standard deviation of o=20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of
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