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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.
2 1/3 + 3 3/8
how can we prove that an absolute convergent series is convergent but the converse is not true.
Five more than the quotient of a number and 2 is at least that number. What is the greatest value of the number? Let x = the number. Notice that quotient is a key word for div
S IMILAR TRIANGLES : Geometry is the right foundation of all painting, I have decided to teach its rudiments and principles to all youngsters eager for ar
41x + 53y = 135, 53x +41y =147 Ans: 41x + 53 y = 135, 53 x + 41 y = 147 Add the two equations : Solve it, to get ... x + y = 3 -------(1) Subtract : Solve it , to
11-b=34
Graph f ( x ) = - x 2 + 2x + 3 . Solution It is a parabola in the general form. f ( x ) = ax 2 + bx + c In this form, the x-coor
Example Find the Highest Common Factor of 54, 72 and 150. First we consider 54 and 72. The HCF for these two quantities is calculated as follows:
Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c
What are the Input and Output of Marketing
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