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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.
Explain some Examples of linear in - Equation, with solution.
The Dolphins football team gained 16 yards on their first play then lost 11 yards on the next play. Write an addition expression to represent this situation.Find the sum an explain
Let m be a positive integer with m>1. Find out whether or not the subsequent relation is an equivalent relation. R = {(a,b)|a ≡ b (mod m)} Ans: Relation R is illust
What are some equations for 36?
1 ream uses 6% of a tree, Estimate the reams of paper used in one month in an office(may be your father, mother or neighbour), hence find the number of trees that need to be cut fo
Fourier series - Partial Differential Equations One more application of series arises in the study of Partial Differential Equations. One of the more generally employed method
Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8
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Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t
A fire in a building B is reported on telephone to two fire stations P and Q, 10km apart from each other on a straight road. P observes that the fire is at an angle of 60 o to th
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