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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.
Vector Functions We very firstly saw vector functions back while we were looking at the Equation of Lines. In that section we talked about them as we wrote down the equation o
In a group of 85 people, 33 own a microwave, 28 own a DVD player and 38 own a computer. In addition, 6 people own both a microwave and a DVD player, 9 own both a DVD player and a c
Determine all possible solutions to the subsequent IVP. y' = y ? y(0) = 0 Solution : First, see that this differential equation does NOT satisfy the conditions of the th
Danielle requires knowing the distance around a basketball court. What geometry formula will she use? The perimeter of a rectangle is two times the length plus two times the wi
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Let's start things by searching for a mixing problem. Previously we saw these were back in the first order section. In those problems we had a tank of liquid with several kinds of
R={(r, ?):1=r= 2cos? ,-p/3= ? =p/3
A,B,C are natural numbers and are in arithmetic progressions and a+b+c=21.then find the possible values for a,b,c Solution) a+b+c=21 a+c=2b 3b=21 b=7 a can be 1,2,3,4,5,6 c c
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Characteristics of Exponential Smoothing 1. More weight is described to the most recent data. 2. All past data are incorporated not like in moving averages. 3. Les
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