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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.
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y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64 Solution : As we noticed in previous illustration the function is a solution an
Classical Probability Consider the experiment of tossing a single coin. Two outcomes are possible, viz. obtaining a head or obtaining a tail. The probability that it is a tail
The students at Norton School were asked to name their favorite type of pet. Of the 430 students surveyed, 258 said in that their favorite type of pet was a dog. Assume that only 1
Bill spent 50% of his savings on school supplies, and then he spent 50% of what was left on lunch. If he had $6 left after lunch, how much did he have in savings at the starting?
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A computer is programmed to scan the digits of the counting numbers.For example,if it scans 1 2 3 4 5 6 7 8 9 10 11 12 13 then it has scanned 17 digits all together. If the comput
a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950
If tanA+sinA=m and m2-n2 = 4vmn, show that tanA-sinA=n
How do i divide 200 by 4
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