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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.
who ,why and when discovered unitary method
Determine and classify all the critical points of the given function. Described the intervals where function is increasing & decreasing. Solution: Firstly we'll require
Q UADRATIC EQUATIONS: For the things of this world cannot be made known without a knowledge of mathematics. Solve by factorization a. 4x 2 - 4a 2 x +
i dont understand angels and lines
Ahmad borrowed $450000.00 at 3% compounded semi-annually for ten years to buy an apartment. Equal payments are made at the end of every six months. a) Determine the size of the se
one half y minus 14
Right- and left-handed limits : Next, let's see precise definitions for the right- & left-handed limits. Definition For the right-hand limit we say that, if for eve
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Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans: Given : - ∠APB = 120o Construction : -Join OP To prove : -
Bob is 2 years from being double as old as Ellen. The sum of twice Bob's age and three times Ellen's age is 66. How old is Ellen? Let x = Ellen's age and let y = Bob's age. Sin
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