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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;
These can be expressed in terms of two fundamental operations of addition and multiplication. If a, b and c are any three real numbers, then; 1.
1. Let A = {1,2, 3,..., n} (a) How many relations on A are both symmetric and anti-symmetric? (b) If R is a relation on A that is anti-symmetric, what is the maximum number o
If a, b and c are in harmonic progression with b as their harmonic mean then, b = This is obtained as follows. Since a, b and c are in
Solve the inequality |x - 1| + |x - 2|≤ 3. Working Rule: First of all measure the expression to zero whose modulus happens in the given inequation and from this search the va
An IVP or Initial Value Problem is a differential equation with an appropriate number of initial conditions. Illustration 3 : The subsequent is an IVP. 4x 2 y'' + 12y' +
On a picnic outing, 2 two-person teams are playing hide-and-seek. There are four hiding locations (A, B, C, and D), and the two peoples of the hiding team can hideseparately in any
1) Find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2) Compute the work done by the force ?eld F(x,y,z) = x^2I + y j +y k in moving
mean absolue deviation
1. Find the slope and the y-intercept of the line whose equation is 5x + 6y = 7. 2. Find the equation of the line that is parallel to 2x + 5y = 7 and passes through the mid poin
a muffin recipe calls for three forth of a cup of sugar and one eight of a cup of butter. travis accidentally put in one whole cup of butter. how much sugar does travis need to put
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