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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.
Identify the surface for each of the subsequent equations. (a) r = 5 (b) r 2 + z 2 = 100 (c) z = r Solution (a) In two dimensions we are familiar with that this
The 3-D Coordinate System We will start the chapter off with a quite brief discussion introducing the 3-D coordinate system and the conventions that we will be utilizing. We
Lines EF and GH are graphed on this coordinate plane. Which point is the intersection of lines EF and GH?
Cylindrical Coordinates - Three Dimensional Space Since with two dimensional space the standard (x, y, z) coordinate system is known as the Cartesian coordinate system. In the
$112 in 8 hours
Q. Find Probability of tossing a head with the dime? List the sample space, and find n(S), for the outcomes of tossing a nickel followed by a dime. What is the probability of t
Classical Probability Consider the experiment of tossing a single coin. Two outcomes are possible, viz. obtaining a head or obtaining a tail. The probability that it is a tail
The equation ax2 + 2hxy + by2 =0 represents a pair of straight lines passing through the origin and its angle is tan q = ±2root under h2-ab/(a+b) and even the eqn ax2+2hxy+by2+2gx+
Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
Define a Hamilton path. Determine if the following graph has a Hamilton circuit. Ans: A path is known as a Hamiltonian path if it consists of every vertex of the graph e
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