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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;
in the quadrilateral abcd,ab is 4.3,bd is 5.1,ad is 4.8.angle bdc is 20 degrees and angle c is 80 degrees.all dimentions in metres.calculate the unknown sides and angles of the plo
express each logariths in terms of log3 P and log3 Q. 1. log3 P^2 Q^3
in the horizontal bar event the u.s.a scored 28.636,gremany scroed 28.7,romnia scored 27.962,and chain scored 28.537 points.which list shows these scored in descending order
We here move to one of the major applications of differential equations both into this class and in general. Modeling is the process of writing a differential equation to explain a
Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
would like explaination on how to do them
Find out the number of ways in which 5 prizes can be distributed among 5 students such that (a) Each student may get a prize. (b) There is no restriction to the number o
In an equilateral triangle 3 coins of radius 1cm each are kept along such that they touch each other and also the side of the triangle. Determine the side and area of the triangle.
Find the Quadratic polynomial whose sum and product of zeros are √2 + 1, 1/ √2 + 1 Ans: sum = 2 √2 Product = 1 Q.P = X 2 - (sum) x + Product ∴ x 2 - (2 √2 )
what is 6/36 as two equivalent fractions 2/12 as two equivalent fractions 4/28 3/21 2/11 4/13=8/x 12/30=n/90 q/54=2/9 3/7 14/h=7/20
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