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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 oranges are bought at the rate of 11 for rupees 10 and are sold at the rate of 10 for rupees 11, find the profit percent
castor brought 6 3/4 carat cakes to share with 26 students. did castor bring enough for each student to have 1/4 of cake?
INTRODUCTION : Most of us, when planning the first mathematical experience for three-year olds, think in terms of helping them memorise numbers from 1 to 20. We also teach them to
Describe Order of Operations with example? The order of operations is a set of rules that describe the order in which math operations are done. Try doing this math problem:
Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t
If n is positive integer greater than 1 and a & b both are positive real numbers then, Consider that on occasion we can let a or b to be negative and yet have these propert
how to do mathematical proofs
Divides a given line segment internally in the ratio of 1:3 Construction : i )Draw a ray AX making an acute angle with AB. ii) Mark 4 points at equal distance. on AX Let
51/6 divided by 31/3
What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32
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