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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.
Prove that the Digraph of a partial order has no cycle of length greater than 1. Assume that there exists a cycle of length n ≥ 2 in the digraph of a partial order ≤ on a set A
find the area bounded by the curve y=5x^2-4x+3 from the limit x=0 to x=5
want to make an assignment on shares and dividend for class 10
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
evaluate sin 15
Find the remainder when 7^103 is divided by 24 Solution) we know by the concept of mod that..... 49 is congruent to 1 mod 24(means if 1 is subtracted fom 49 u get 48 which is
If the M-th term of an Ap is n andn-th term M.find the p-th term
Properties of Cross product If u, v and w are vectors and c is a number then u → * v → = -v → * w → (cu → ) * v → =
A train goin from delhi to jaipur stops at 7 intermediate stations. 5 persons enter the train during the journey with 5 difefrent tickets of same class . How mant different set of
Write following in terms of simpler logarithms. (a) log 3 (9 x 4 / √y) Solution log 3 (9 x 4 / √y) =log 3 9x 4 - log y (1/2) =log 3 9 + log 3 x 4
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