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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.
Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t
Find the greatest number of 6 digits exactly divisible by 24, 15 and 36. (Ans:999720) Ans: LCM of 24, 15, 36 LCM = 3 × 2 × 2 × 2 × 3 × 5 = 360 Now, the greatest six digit
which ne is greater -4 4/25 or -4.12?
Demonstrate that Dijkstra's algorithm does not necessarily work if some of the costs are negative by finding a digraph with negative costs (but no negative cost dicircuits) for whi
if x+y+z=pi=180 prove that sin^2x+sin^2y+sin^z-2sinx*siny*sinz=2
Find out the number of ways in which 5 prizes can be distributed among 5 students such that (a) Each student may get a prize. (b) There is no restriction to the number o
"Standard" trig equation: Now we need to move into a distinct type of trig equation. All of the trig equations solved to this point were, in some way, more or less the "standard"
Patrick gets paid three dollars less than four times what Kevin gets paid. If the number of dollars which Kevin gets paid is represented through x, what does Patrick get paid?
Finding the number of Permutations of 'n' dissimilar things taken 'r' at a time: After looking at the definition of permutations, we look at how to evolve a
what is the LCM of 18, 56 and 104 show working
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