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lim n tends to infintiy ( {x} + {2x} + {3x}..... +{nx}/ n2(to the square) )where {X} denotes the fractional part of x?Ans) all no.s are positive or 0. so limit is either positive or 0.........(1)now {x}<=1;{2x}<=1;......{x}+{2x}+....{nx}<=nthat implies lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity n/n^2;that means lim n tends to infinity{x}+{2x}+....{nx}/n^2 <= lmit n tends to infinity 1/n i.e. 0........(2)from (1) and (2);required limit=0;
if 2+2=4 what does two times two epual?
what is the differeance in between determinate and matrix .
Advantages And Limitations Of Game Theory Advantage Game theory assists us to learn how to approach and understand a conflict condition and to develop the decision making
Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o
We can define the conditional probability of event A, given that event B occurred when both A and B are dependent events, as the ratio of the number of elements common in both A an
Obligatory application/interpretation problem : Next, we need to do our obligatory application/interpretation problem so we don't forget about them. Example : Assume that the
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
Solve for x , y (x + y - 8)/2 =( x + 2 y - 14)/3 = (3 x + y - 12 )/ 11 (Ans: x=2, y=6) Ans : x+ y - 8/2 = x + 2y - 14 /3 = 3x+ y- 12/11
Find the area enclosed between two concentric circles of radii 3.5cm, 7cm. A third concentric circle is drawn outside the 7cm circle so that the area enclosed between it and the 7
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