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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;
Explain Identifying Conic Sections The graph of a quadratic equation in the variables x and y, like this one, x 2 + 3y 2 + 6y = -4, is a conic sections. There are three kind
solving sums
A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days. The remaining 2 days may be any of the following : (i) Sunday and Monday (ii) Monday and Tuesday (iii)
approximate the following problem as a mixed integer program. maximize z=e-x1+x1+(x2+1)2 subject to x12+x2 =0
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Chain Rule : We've seen many derivatives. However, they have all been functions similar to the following kinds of functions. R ( z ) = √z f (t ) = t 50
Question: Use Gauss elimination method to solve the following system of equations. -y +3z=4 2x-y-2z= 2 2x-2y+z =6 4x-y-7z= 0
let setM={X,2X,4X} for any numberX .if average (arthemetic mean)of the number in setM is 14.what is the value of X?
Repetition Need Not Be Boring : From an early age on, children engage in and learn from repetitive behaviour, such as dropping and picking up things, opening and closing boxes an
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