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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.
Trace the curve (x/a)^3/2+(y/b)^2/3=1
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What is minimum spanning tree? Determine a railway network of minimal cost for the cities in the following graph using Kruskal's algorithm. Ans: Minimum spanning tree in a con
-x^3+6x-7
Find the solution to the subsequent IVP. ty' - 2y = t 5 sin(2t) - t 3 + 4t 4 , y (π) = 3/2 π 4 Solution : First, divide by t to find the differential equation in the accu
Type I and type II errors When testing hypothesis (H 0 ) and deciding to either reject or accept a null hypothesis, there are four possible happenings. a) Acceptance of a t
Standardizing a Random Variable If X is a random variable with E(X) = m and V(X) = s 2 , then Y = (X – m)/ s is a random variable with mean 0 and standard deviatio
Price Cutter sold 85 beach towels for $6.95 each. What were the total sales? You must multiply the number of towels sold through the price of each towel; 85 × $6.95 = $590.75.
A telephone company charges $.35 for the first minute of a phone call and $.15 for each additional minute of the call. Which of the subsequent represents the cost y of a phone call
Eliminate the parameter from the subsequent set of parametric equations. X = t 2 + t Y = 2t - 1 Solution: One of the very easy ways to eliminate the parameter is to
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