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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;
joey asked 30 randomly selected students if they drank milk, juice, or bottled water with their lunch. He found that 9 drank milk, 16 drank juice, and 5 drank bottled water. If the
Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po
(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy
Partial Fraction Decomposition The procedure of taking a rational expression and splitting down it into simpler rational expressions which we can add or subtract to get the ori
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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?
Determine the measure of the vertex angle of the isosceles triangle. a. 34° b. 16° c. 58° d. 112° d. Simply substitute x = 34 into the equation for the vertex angle,
1a.if the williams spend $385 a month on food what is their monthly income
What is Plotting Points? To "plot" or "graph" values means to find points on a number line. The numbers four, negative two, negative three, zero, two, and negative four are bei
Decision Theory Decisions There are many types of decision making 1. Decision making under uncertainty It refer to situations where more than one outcome can r
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