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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.
Prove that the Digraph of a partial order has no cycle of length greater than 1. Assume that there exists a cycle of length n ≥ 2 in the digraph of a partial order ≤ on a set A
chapter permutation & combination ex :4.6
Interpretation of r - Problems in interpreting r values A high value of r as +0.9 or - 0.9 only shows a strong association among the two variables but doesn't imply that th
Reasons why we start division : The reason we start division by considering the digit in the leftmost place is efficiency and ease . For instance, suppose we divide 417 by 3, we
Martha has $20 to spend and would like to buy as several calculators as possible along with the money. The calculators that she needs to buy are $4.50 each. How much money will she
The probability that a randomly selected 3-year old garter snake will live to be 4 years old is .54 (assume results are independent). What is the probability that five randomly se
three prices are to be distributed in a quiz contest.The value of the second prize is five sixths the value of the first prize and the value of the third prize is fourfifth that of
Find the series solution of2x2y”+xy’+(x2-3)Y=0 about regular singular pointuestion..
You are painting the surface of a silo that has a diameter of 16 ft and height of 50 ft. What is the net surface area to be painted? Consider the top of the silo is 1/2 a sphere
Q. Difference between Probability and statistics? Ans. Probability and statistics are used in many different aspects of life. What are they and why are they so popular?
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