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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.
Don't count the number of divisions. Do not use asymptotic notation, instead provide exact answers. (i) What is the maximum number of multiplications required to solve a system
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The sum of two consecutive integers is 41. What are the integers? Two consecutive integers are numbers in sequence like 4 and 5 or -30 and -29, that are each 1 number apart. Le
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Q. Samantha wrote a computer program to randomly generate two-digit numbers between 00 and 99. Let X be the random 2 digit number generated by the computer. Find the distributio
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f Y is a discrete random variable with expected value E[Y ] = µ and if X = a + bY , prove that Var (X) = b2Var (Y ) .
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