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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.
Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution: There are 26 ways of choosing the first lett
Question. Determine the position and nature of stationary points of the function? f(x,y)= y/x -x 2 +y 2
1) let R be the triangle with vertices (0,0), (pi, pi) and (pi, -pi). using the change of variables formula u = x-y and v = x+y , compute the double integral (cos(x-y)sin(x+y) dA a
Properties 1. ∫ b a f ( x ) dx = -∫ b a f ( x ) dx . We can interchange the limits on any definite integral, all that we have to do is tack a minus sign onto the integral
Define Markov process. Markov process is one in which the future value is independent of the past values, given the current value
Find the normalized differential equation which has {x, xex} as its fundamental set
a. Estimate the following model, C t = β 0 + β 1 * DI t + ε t Where C t = Aggregate Consumption Expenditure in Australia, quarterly data for the per
find the sum of the following series upto n terms: 1*2+2*4+3*8+4*16+.....
How should shoppers''stop develop its demand forecasts?
solutions for the equation a-b=5
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