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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.
Let R be the relation on S = {1, 3, 6, 9, 27} defined by aRb iff a|b. (a) Write down the matrix of R. (b) Draw the digraph of R. (c) Explain whether R is reflexive, irrere
Interesting relationship between the graph of a function and the graph of its inverse : There is one last topic that we have to address quickly before we leave this section. Ther
In a certain class, one half of the male students and two thirds of the female students speak French. If there are three fourths as many girls as boys in the class. What fraction o
Solution by Factorization, please solve quadratic equations by Factorization.
Determine the slope following lines. Sketch the graph of line. The line which contains the two points (-2, -3) and (3, 1) . Solution we'll need to do is employ
A box is 30 cm long, 8 cm wide and 12 cm high. Determine the length of the diagonal AB ? Round to the nearest tenth. a. 34.5 cm b. 32.1 cm c. 35.2 cm d. 33.3 cm
applications of VAM.
All numbers refer to exercises (and not "computer exercises") in Gallian. §22: 8, 16, 22, 24, 28, 36. In addition: Problem 1: Let a be a complex root of the polynomial x 6 +
(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy
25 cl=____________L
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