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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.
1,5,14,30,55 find the next three numbers and the rule
Curvature - Three Dimensional Space In this part we want to briefly discuss the curvature of a smooth curve (remind that for a smooth curve we require → r′ (t) is continuou
(1) Show that the conclusion of Egroff's theorem can fail if the measure of the domain E is not finite. (2) Extend the Lusin's Theorem to the case when the measure of the domain E
TWO PERSONS A AND B AGREE TO MEET AT A PLACE BTWEEN 11 TO 12 NOON. THE FIRST ONE TOARRIVE WAITS FOR 20 MIN AND THEN LEAVE. IF THE TIME OF THIR ARRIVAL BE INDEPENDET AND AT RNDOM,T
General approach of Exponential Functions : Before getting to this function let's take a much more general approach to things. Let's begin with b = 0 , b ≠ 1. Then an exponential f
Cathy is forming a quilt out of fabric panels that are 6 in through 6 in. She needs to know the total area of her square-shaped quilt. Which formula will she use? The area of a
8l550ml - 1/4l =
If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans: AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A
A and B can finish a piece of work in 16 days and 12 days respectively.A started a work and worked at it for 2 days.He was then joined by B.Find the total time taken to finish the
Prove that one of every three consecutive integers is divisible by 3. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1, 3q +
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