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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.
what is commercial mathematics profit and loss
Elliptic Paraboloid The equation which is given here is the equation of an elliptic paraboloid. x 2 /a 2 + y 2 /b 2 = z/c Like with cylinders this has a cross section
Tangent, Normal and Binormal Vectors In this part we want to look at an application of derivatives for vector functions. In fact, there are a couple of applications, but they
Jocelyn has 6 birds, Their mean age is 10. The mode of their ages is 8. What might their ages be? Show your work.
Evaluate distance traveled by train: A plane flying at 525 miles per hour completes a trip in 2 hours less than another plane flying at 350 miles per hour. What is the distan
Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.
#question Show that the enveloping cylinder of the conicoid ax 2 + by 2 + cz 2 = 1 with generators perpendicular to the z-axis meets the plane z = 0 in parabolas
1. Consider the trigonometric function f(t) = (a) What is the amplitude of f(t)? (b) What is the period of f(t)? (c) What are the maximum and minimum values attained by
Two events A and B are independent events if the occurrence of event A is in no way related to the occurrence or non-occurrence of event B. Likewise for independent
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