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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;
Euler's Method Up to this point practically all differential equations which we've been presented along with could be solved. The problem along with this is which the exceptio
The functions {sinmx; cosmx}; m = 0,....∞ form a complete set over the interval x ∈ [ -Π, Π]. That is, any function f(x) can be expressed as a linear superposition of these
Prove: 1/cos2A+sin2A/cos2A=sinA+cosA/cosA-sinA
Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers
The Mean Value Theorem : In this section we will discuss the Mean Value Theorem. Before we going through the Mean Value Theorem we have to cover the following theorem. Ro
From a sheet of cardboard in the shape of a square of side 14 cm, a piece in the shape of letter B is cut off. The curved side of the letter consists of two equal semicircles & the
The division algorithm says that when a is divided by b, a unique quotient and remainder is obtained. For a fixed integer b where b ≥ 2, consider the function f : Z → Z given by f(
what is the difference between North America''s part of the total population and Africa''s part
Y=θ[SIN(INθ)+COS(INθ)],THEN FIND dy÷dθ. Solution) Y=θ[SIN(INθ)+COS(INθ)] applying u.v rule then dy÷dθ={[ SIN(INθ)+COS(INθ) ] dθ÷dθ }+ {θ[ d÷dθ{SIN(INθ)+COS(INθ) ] } => SI
If the areas of two sections of a garden are 6a + 2 and 5a, what is the difference among the areas of the two sections within terms of a? Because the question asks for the diff
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