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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;
The general solution of the differential equation (dy/dx) +x^2 = x^2*e^(3y). Solution)(dy/dx) +x^2 = x^2*e^(3y) dy/dx=x 2 (e 3y -1) x 2 dx=dy/(e 3y -1) this is an elementar
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Q. Example of circle graphs? Ans. The United States Government pays obligations annually, called "outlays". Medicare contributes to the health and well being of aged an
what is fraction?
Linear Equations We'll begin the solving portion of this chapter by solving linear equations. Standard form of a linear equation: A linear equation is any equation whi
If tanx+secx=sqr rt 3, 0 Ans) sec 2 x=(√3-tanx) 2 1+tan 2 x=3+tan 2 x-2√3tanx 2√3tanx=2 tanx=1/√3 x=30degree
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
Temperature: On one day in Fairfield, Montana the temperature dropped 80 degree fahrenheit from noon to midnight. If the temperature at midnight was -21 degree fahrenheit, write an
a wheel revolves 360 deegre revolution in one minute .Find how many radians will the wheel subtend in one second
1) A local factory makes sheets of plywood. Records are kept on the number of mild defects that occur on each sheet. Letting the random variable x represent the number of mild de
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