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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.
Give an example of each of the following given below . You do not require to give any justication. (a) A nonempty, bounded subset of Q with no inmum in Q. (b) A subspace of
Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120 o . Prove that OP=2AP. Ans: Given : - ∠APB = 120o Construction : -Join OP To prove : -
Applications of derivatives : At last, let's not forget about our applications of derivatives. Example Assume that the amount of air in a balloon at any time t is specified
If the radius of a sphere is doubled, the surface area is a. multiplied by 4. b. multiplied by 2. c. multiplied by 3. d. multiplied by 8. a. The formula for the surf
There are really three various methods for doing such integral. Method 1: This method uses a trig formula as, ∫sin(x) cos(x) dx = ½ ∫sin(2x) dx = -(1/4) cos(2x) + c
for what value of k,the following system of equations have infinite solutions?kx + 5y -(k-5)=0;20x +ky - k=0
Dinesh bought an article for Rs. 374, which included a discount of 15% on the marked price and a sales tax of 10% on the reduced price. Find the marked price of the article.
How do I convert metric units?
Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 3.
A farmer grows apples on her 400-acre farm and must cope with occasional infestations of worms. If she refrains from using pesticides, she can get a premium for "organically grown"
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