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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.
Q. Suppose Jessica has 10 pairs of shorts and 5 pairs of jeans in her drawer. How many ways could she pick out something to wear for the day? What is the probability that she pick
1. A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side
The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of the other two vertices.
Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero. So, let ε 0 so that the following will be true. |x 2 - 0|
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
Theorem Consider the subsequent IVP. y′ = p (t ) y = g (t ) y (t 0 )= y 0 If p(t) and g(t) are continuous functions upon an open interval a o , after that there i
Find the area of shaded region, if the side of square is 28cm and radius of the sector is ½ the length of side of square.
what is slope
Graph ( x + 1) 2 /9 -( y - 2) 2 /4 =1 Solution It is a hyperbola. There are in fact two standard forms for a hyperbola. Following are the basics for each form. H
how to curve trace? and how to know whether the equation is a circle or parabola, hyperbola ellipse?
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