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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.
Find out the roots of the following quadratic equation. 3x 2 + 7x = 0 Solution: Using Equation 6, one root is determined. x = 0 Using Equation 7, substitute the
The product on multiplying - 4bc with 2a is - 8abc. That is, a term with minus sign multiplied with a term having a positive term gives a product which has a minus sign. On the
identify the range of h(x)=2x+1
find middle term [2a-a2/4]9
A discrete-valued random variable X takes values in 0, 1, 2, . . . , where p(X = i) = π i. (a) Write down formulas for: the p-value at X = i the probability distributi
Independent and Dependent Events Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event
1000 time 1000000
A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Findout the quantity of every solutions to get the resultant mixture.
Give a Definition of Perimeter and Area? Perimeter is the distance around a flat (2-dimensional) shape. Area is the amount of space taken up by a flat (2-dimensional) shape. is
Problem: A person has 3 units of money available for investment in a business opportunity that matures in 1 year. The opportunity is risky in that the return is either double o
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