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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;
Three payments of $2000 (originally due six months ago, today, and six months from now) have been renegotiated to two payments: $3000 one month from now and a second payment due in
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Describe and sketch the surfaces z + |y| = 1 and (x 2) 2 y + z 2 = 0.
(a) Assume that A is a m 1 ×m 2 matrix and B is a m 2 ×m 3 matrix. How many multiplications are required to calculate the matrix product AB? (b) Given that A 1 is a 20 × 50 m
which laws of physics are used to discuss heat loss in a pipe
Question Suppose that f(x) has (x - 2) 2 and (x + 1) as its only factors. Sketch the graph of f. State all the zeros of f.
what is sandwich throem
5a^2b^2-5ab(6)
Proof of Sum/Difference of Two Functions : (f(x) + g(x))′ = f ′(x) + g ′(x) It is easy adequate to prove by using the definition of the derivative. We will start wi
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