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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.
Repetition Need Not Be Boring : From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an
what are 20 integer equations that have multiplication, division, subtraction,and additon??
Rob purchased picnic food for $33.20 to share along with three of his friends. They plan to split the cost evenly among the four friends. How much does every person required to pay
Although the set of integers caters to a larger audience, it is inadequate. This inadequacy has led to the formulation of Rational numbers. Rational numbers are of
At an office, the manager earns 40% more than a first year employees. The employee earns what fraction of the manager earnings?
The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that dy dx vanishes for some value of x in the interval -1≤x≤1?
An elliptical galaxy has gravitational boundaries defiend by 9x 2 +16y 2 +144z 2 =144. A black hole at the center of the galaxy is interacting with dark matter producing a radiatio
what is the difference between North America''s part of the total population and Africa''s part
Type I and type II errors When testing hypothesis (H 0 ) and deciding to either reject or accept a null hypothesis, there are four possible happenings. a) Acceptance of a t
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