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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;
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UNDETERMINED COEFFICIENTS The way of Undetermined Coefficients for systems is pretty much the same to the second order differential equation case. The simple difference is as t
Ravi is a teacher of Class 4 in a municipal school in Delhi. When the new school year started, he opened the textbook and started teaching the children how to write 4-digit numbers
the sum of the interior angles of a convex rectilinear figure is equal to sum of the exterior angles. then the number of sides is
Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe
Domain of a Vector Function There is a Vector function of a single variable in R 2 and R 3 have the form, r → (t) = {f (t), g(t)} r → (t) = {f (t) , g(t), h(t)} co
the function g is defined as g:x 7-4x find the number k such that kf(-8)=f- 3/2
200000+500
Utilizes the definition of the limit to prove the given limit. Solution In this case both L & a are zero. So, let ε 0 so that the following will be true. |x 2 - 0|
Is prerequisite multipcation or addition
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