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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.
Use Newton's Method to find out an approximation to the solution to cos x = x which lies in the interval [0,2]. Determine the approximation to six decimal places. Solution
Express the product of -9p3r and the quantity 2p - 3r in simplified form. The translated expression would be -9p3r(2p - 3r). Noticed that the key word product means multiply.
The dimensions of a rectangular prism can be expressed as x + 1, x - 2, and x + 4. In terms of x, what is the volume of the prism? Since the formula for the volume of a rectang
What do you mean by transient state and steady-state queueing systems If the characteristics of a queuing system are independent of time or equivalently if the behaviour of the
The square of a positive number is 49. What is the number? Let x = the number. The sentence that is , "The square of a positive number is 49," translates to the equation x 2
a company of 10000 shares of rs 100 each declares a annual dividend of 5 %.what is the total amount dividend paid by the company
A spring has a natural length of 20 Centimeter. A 40 N force is needed to stretch and hold the spring to a length of 30 Centimeter. How much work is completed in stretching the spr
In how many ways 30 identical balls can be DISTRIBUTED among 4 boys?? Ans) Let they get a,b,c,d respectively. You requireto find the non negative integral results of a+b+c+d=3
The Limit : In the earlier section we looked at some problems & in both problems we had a function (slope in the tangent problem case & average rate of change in the rate of chan
Q. Define Number Line? Ans. A number line is a nice way to visualize and examine the ordering of the positive and negative numbers. Every positive and negative number that
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