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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.
If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro
1+2+3+.....+n=1/2n(n+1)
Sequences and Series In this section we will be taking a look at sequences and infinite series. In fact, this section will deal approximately exclusively with series. Though
Q. Negative Signs in Fractions? It really doesn't matter where you put a negative sign in a fraction. The following are all the same: The negative sign can go in
1 1/3:2/3:1/6
Consider two bags, A and B, with the following contents Bag A Bag B 3 white marbles 4 white marbles 2 red marbles
Susan traveled 114 miles in 2 hours. If she remains going at the similar rate, how long will it take her to go the remaining 285 miles of her trip? There is a 1 in 6 chance of
of all those survey 390 were under 18 years of age if 20%were 18, how many responded to the survey
Horizontal asymptotes : Such as we can have vertical asymptotes defined in terms of limits we can also have horizontal asymptotes explained in terms of limits. Definition
Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To beg
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