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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.
how do you find the distance between the sun and earth
A right triangular prism has volume equal to 288 cm^3. The height of the prism is 3 cm. One of the bases of the triangular face (not the hypotenuse) is equal to 12 cm, determine th
Equation s(in Tth second)=u+at-a/2 seems to be dimensionally incorrect.why?
DEVELOPMENT IS CONTINUOUSLY GOING ON : Think of any two children around you. Would you say that they are alike? Do they learn the same things the same way? It is very unlikely be
suresh invested rs.1080 in shares of face value rs.50 at rs.54.After receiving dividend on them at 8% he sold them at 52.In each of the transaction he paid 2 % brokerage.Hpw much d
The boundary of the shaded portion in the adjoining figure consists of our half-circles and two quarter-circles. Find the length of the boundary and the area of the shaded portion
Repetition Need Not Be Boring : From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an
larry spends 3/4 hours twice a day walking and playing with his dog. He spends 1/6 hours twice a day feeding his dog. how much time does larry spend on his dog each day?
Indeterminate forms Limits we specified methods for dealing with the following limits. In the first limit if we plugged in x = 4 we would get 0/0 & in the second limit
The HCF & LCM of two expressions are respectively (x+3) and (x cube-7x+6). If one is x square+2x-3 , other is? Solution) (x+3) * (x^3-7x+6) = (x^2+2x-3) * y ( ) (HCF*LCM=
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