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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.
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Define Markov chain Random processes with Markov property which takes separate values, whether t is discrete or continuous, are known as Markov chains.
Find the number of six-digit positive integers that can be formed using the digits 1,2, 3, 4, and 5 (every of which may be repeated) if the number must start with two even digits o
terminology and requirements of linear programming
Even and Odd Functions : This is the final topic that we have to discuss in this chapter. Firstly, an even function is any function which satisfies,
Plot the points A(2,0) and B (6,0) on a graph paper. Complete an equilateral triangle ABC such that the ordinate of C be a positive real number .Find the coordinates of C (Ans: (
The arm of a ceiling fan measures a length of 25 in. What is the area covered through the motion of the fan blades while turned on? (π = 3.14) The ceiling fan follows a circula
The frequency of oscillation of an object suspended on a spring depends on the stiffness k of the spring (called the spring constant) and the mass m of the object. If the spring is
MAKING CONNECTIONS : you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo
who discovered unitary meathod
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