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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.
Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers [7] 2.2 In a given day he will sel
Determine the derivative of the following function by using the definition of the derivative. f ( x ) = 2 x 2 -16x + 35 Solution Thus, all we actually have to do is to pl
Prove that if x is a real number then [2x] = [x] + [x + ½ ] Ans: Let us consider x be any real number. It comprises two parts: integer and fraction. With no loss of
Evaluate the given limit. Solution: In this question none of the earlier examples can help us. There's no factoring or simplifying to accomplish. We can't rationalize &
A reliability system consists of 15 independent components. The probability that a component works is 0.9 for each. The system works if at least 11 of the components work. Fi
Need help figuring perimeter and area.
a research on area of plane figures
Simplify the logical expression X‾ Y‾ + X‾ Z + Y Z +Y‾ Z W‾ Ans: The K-Map for the following Boolean expression is described by the following diagram. The optimized expression
the traffic light at three different road crossing change after every 48 seconds, 72 seconds and 108 seconds respectively. if they change simultaneously at 7 a.m., at what time wil
Objectives After studying this unit, you should be able to 1. evolve and use alternative activities to clarify the learner's conceptual 2. understanding of ones/tens/hu
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