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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.
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At times we consider only the magnitude of the number without attaching much importance to its direction. Under these circumstances the sign attached with the num
Differentiate following functions. (a) f ( x ) = 2 x 5 cosh x (b) h (t ) = sinh t / t + 1 Solution (a) f ′ ( x ) = 10x 4 cosh x + 2x 5 sinh x (b) h′ (t ) = (t
Simple Random Sampling It refers to the sampling technique whether each and every item of the population is described an equal chance of being included in the sample. Because s
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Eileen needs 9 feet of fabric to make a skirt. If Eileen has 18 feet of fabric how many skirts can she make?
statement of gauss thm
Example Find the values of the given expressions. Also given that a = 2, b = 3, c = 1, and x = 2. 8a + 5bc = 8.2
The area of a parallelogram is x 8 . If the base is x 4 , what is the height in terms of x? Since the area of a parallelogram is A = base times height, then the area divided by
Circle Well, let's recall just what a circle is. A circle is all the points which are the similar distance, r - called the radius, from a point, ( h, k ) - called the center. I
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