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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.
What are Factors? When you multiply several numbers together, (4 x 5 x 3), the numbers (4, 5, and 3) being multiplied are called factors. The result of the multiplying th
If r,R denote position vectors of points on the straight lines in the direction of a and b respectively, and if n is a unit vector perpendicular to both these directions, show that
Solve the subsequent IVP and find the interval of validity for the solution. y' + (4/x) y = x 3 y 2 , y(2) = - 1, x > 0 Solution Thus, the first thing that we re
THE FIRST AND THIRD TERM OF A G.P ARE 8 AND 18 RESPECTIVELY AND THE COMMON RATIO IS POSITIVE.FIND THE COMMON RATIO
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A reaction following first-order kinetics was studied by determining the reactant concentrations at equal time intervals. Each successive pair of concentrations, [A] o and [A] 1
#k1=f(Tn, Xn), k2=f (Tn + H.Y,Xn + H.Y.k1) Xn+1=Xn + H(a.k1+ b.k2) Find a relation between Y,a and b so that the method is second order consistent.
Two people are 50 feet separately. One of them begin walking north at rate so that the angle illustrated in the diagram below is changing at constant rate of 0.01 rad/min. At what
writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
find h in the parallelogram
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