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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.
Maths For Fun : Often, when I have time on my hands, I try to solve interesting mathematical questions of the following kind. Sometimes my friends and I create the problems, and
Cathy is forming a quilt out of fabric panels that are 6 in through 6 in. She needs to know the total area of her square-shaped quilt. Which formula will she use? The area of a
Build a Fine Automaton which accept all words which have different first and last letters (that is if the word starts with an "a" to be accepted it should end with "b" and vice ver
John was doing his homework on vertical addition, and had to compute : 5 3+ 3 4 and 6 8 +45 He did the first one easily, just the way his teacher had taught him. He first ad
As x tends to zero the value of 1/x tends to either ∞ or -∞. In this situation we will not be sure about the exact value of 1/x. As a result we will not be sure about the exact/app
Find out if the following series is convergent or divergent. Solution There really is not very much to these problems another than calculating the limit and then usin
Two angles are supplementary. The evaluate of one is 30 more than twice the measure of the other. Determine the measure of the larger angle. a. 130° b. 20° c. 50° d. 70
How many square centimeters are in one square meter? There are 100 cm in a meter. A square meter is 100 cm through 100 cm. The area of this is 10,000 sq cm (100 × 100 = 10,000)
dterminant order 3*3
if ab=25 . a(5,x)and b(2,5) . find x.
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