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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.
Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a foot ball match? Ans: equally likely because they are mutual
Q. Mean and Standard Deviation? Ans. The normal distribution is totally described if we know the average and standard deviation. - the population mean of the distribu
#question.As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and hol
Problem 1 Let ~x0 = A~x and y 0 = B~y be two 2 2 linear systems of ODE. (1) Suppose that A and B have the same purely imaginary eigenvalues. Prove that these systems are topologi
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Tom has five times as many marbles as Jim. together they have 42 marbles. how many marbles does each has?
Before going to solving differential equations we must see one more function. Without Laplace transforms this would be much more hard to solve differential equations which involve
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