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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.
Evaluate following. ∫ 0 ln (1 + π ) e x cos(1-e x )dx Solution The limits are little unusual in this case, however that will happen sometimes therefore don't get
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A recipe calls for 2 1/4 teaspoons of salt for every 1 1/8 teaspoons of black pepper used. How many teaspoons of salt are needed for each teaspoon of pepper used ?
If the diameter of a right cylinder is doubled and the height is tripled, its volume is a. multiplied by 12. b. multiplied by 2. c. multiplied by 6 d. multiplied by 3.
Smith keeps track of poor work. Often on afternoon it is 5%. If he checks 300 of 7500 instruments what is probability he will find less than 20 substandard?
QUESTION (a) A bowl contains ten red balls and ten blue balls. A woman selects balls at random without looking at them. i) How many balls must she select to be sure of havin
A researcher is investigating the effectiveness of a new medication for lowering blood pressure for individuals with systolic pressure greater than 140. For this population, systol
The price of heating oil rose from $1.10 per gallon to $1.43 per gallon. What is the percent of increase? The price of heating oil rose $0.33 ($1.43 - $1.10 = $0.33). To ?nd ou
4n to the power 3/2 = 8 to the power minus 1/3. find the value of n.
in the quadrilateral abcd,ab is 4.3,bd is 5.1,ad is 4.8.angle bdc is 20 degrees and angle c is 80 degrees.all dimentions in metres.calculate the unknown sides and angles of the plo
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