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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.
geometry fbw = 128 saf= 104 what is rfd
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nature of operation research
What is 123x456x789
Objectives After going through this unit, you should be able to 1. explain the processes involved ih addition and subtraction; 2. plan and execute activities that woul
If x = b y where both b > 0, x > 0, then we define y = log b x, which is read as "y is the log to the base b of x". This means that, log b x or y is the number to
Example Suppose the demand and cost functions are given by Q = 21 - 0.1P and C = 200 + 10Q Where, Q - Quantity sold
writing sin 3 a.cos 3 a = sin 3 a.cos 2 a.cosa = sin 3 a.(1-sin 2 a).cosa put sin a as then cos a da = dt integral(t 3 (1-t 2 ).dt = integral of t 3 - t 5 dt = t 4 /4-t 6 /6
from 0->1: Int sqrt(1-x^2) Solution) I=∫sqrt(1-x 2 )dx = sqrt(1-x 2 )∫dx - ∫{(-2x)/2sqrt(1-x 2 )}∫dx ---->(INTEGRATION BY PARTS) = x√(1-x 2 ) - ∫-x 2 /√(1-x 2 ) Let
Calculate the area and circumference of a circle: Calculate the area and circumference of a circle with a 3" radius. Solution: A = πr2
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