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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.
Midpoint Rule - Approximating Definite Integrals This is the rule which should be somewhat well-known to you. We will divide the interval [a,b] into n subintervals of equal wid
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.
A box contains 12 balls out of which x are black .if one ball is drawn at random from the box what is the probability that it will be a black ball ? If 6 more black balls are pu
Find the volume of a cylinder of radius r and height h. Solution : Here, as we mentioned before starting this illustration we actually don't require using an integral to get t
A particular algebra text has a total of 1382 pages which is broken up into two parts. the second part of book has 64 more pages than first part. How many pages are in each part of
1/cos(x-a)cos(x-b)
The next kind of problem seems as the population problem. Back in the first order modeling section we looked at several population problems. In such problems we noticed a single po
Prime number A prime number is a number whose only +ve factors are 1 and itself. For instance 2, 3, 5, and 7 are all of the examples of prime numbers. Examples of numbers whic
predict whether there is a relationship between the mean January temperatures of a city in North America and the city''s position west of the prime meridian.
Total Contribution per Year for next 10yeras =$1000+$800 =$1800 So Total Future fund Vaule =$1800*(1+1.073+power(1.073,2)+ power(1.073,2)+ power(1.073,3)+ power(1.073,4)+ power
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