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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.
Question 1: What is the minimum number of students each of whom comes from one of the 50 different states, enrolled in a university to guarantee that there are at least 100 who
x=ct,y=c/t d^2/dx^2
1. What is the value of Φ(0)? 2. Φ is the pdf for N(0, 1); calculate the value of Φ(1.5). 3. Suppose X ~ N(0, 1). Which, if either, is more likely: .3 ≤ X ≤ .4, or .7 ≤ X ≤
program of curve revolve and create a surface
A 100 by 150 mm rectangular plate is deformed as shown in the following figure. All dimensions shown in the figure are in millimeters. Determine at point Q: (a) the strain compone
An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio
three complain forces of magnitudes 20N 30N and 45N
Distance Traveled by Car - word problem: It takes a man 4 hours to reach a destination 1325 miles from his home. He drives to the airport at an average speed of 50 miles per h
Larry purchased 3 pairs of pants for $24 each or have 5 shirts for $18 each. How much did Larry spend? Divide the miles through the time to find the rate; 3,060 ÷ 5 = 612 mph.
Hierarchical Structures : As the abstractions from concrete objects and materials become more and more general, they represent wider and wider ideas. If we put down each step of
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