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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.
Extreme Value Theorem : Assume that f ( x ) is continuous on the interval [a,b] then there are two numbers a ≤ c, d ≤ b so that f (c ) is an absolute maximum for the function and
As office manager of her firm, Marcellyne has been directed to buy new filing cabinets. She knows that cabinet A costs $10, requires 6 square feet of floor space, and holds 9 cubic
Hypergeometric Distribution Consider the previous example of the batch of light bulbs. Suppose the Bernoulli experiment is repeated without replacement. That is, once a bulb is
In parallelogram ABCD, m∠A = 3x + 10 and m∠D = 2x + 30, Determine the m∠A. a. 70° b. 40° c. 86° d. 94° d. Adjacent angles in a parallelogram are supplementary. ∠A a
Consider the function f(x) = x + 1/x 2 + 2x - 3. (a) Find f(2) and f(-2). (b) Find the domain of f(x). (c) Does the range include 1? Show your working. (d) Find and si
Indeterminate forms Limits we specified methods for dealing with the following limits. In the first limit if we plugged in x = 4 we would get 0/0 & in the second limit
a + b
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Look on the web for a data base that can be converted to an undirected graph. For example, in Science there is a data base of proteins and their interactions. Each protein can b
how to present root numbers on a number line
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