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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 A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0. Ans : AP = PB ⇒ AP 2 = PB 2 (∝ + 4) 2
solve and graph the solution set 7x-4 > 5x + 0
For this point we've only looked as solving particular differential equations. Though, many "real life" situations are governed through a system of differential equations. See the
What is Angle Pairs? Two angles are adjacent angles if they have the same vertex and share one side. Vertical angles are a pair of nonadjacent angles formed by two intersecting
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Danny is a contestant on a TV game show. If he gets a question right, the points for that question are added to his score. If he gets a question wrong, the points for that question
1/2+8/9
In the graphical representation of a frequency distribution if the distance between mode and mean is k times the distance between median and mean then find the value of k.
Vertical asymptote Definition : The function f(x) will contain a vertical asymptote at x = a if we contain any of the following limits at x = a . x→a- Note as well that it
Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0
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