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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;
Test of homogeneity This is concerned along with the proposition that several populations are homogenous along with respect to some characteristic of interest for example; one
Dawn wants to evaluate the volume of a basketball along with the volume of a tennis ball. Which formula will she use? The volume of a sphere is 4/3 times π times the radius cub
Evaluate the area of the region. a. 478 units 2 b. 578 units 2 c. 528 units 2 d. 428 units 2 b. Refer to the diagram to evaluate the area of the shaded
The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α .After walking a distance d towards the foot of the tower the angle of elevation is
What is Graphing Statistics explain ? The number of times that an event occurs is called its frequency. One of the ways that you can compare or display different frequencies is
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Newton's Method : If x n is an approximation a solution of f ( x ) = 0 and if given by, f ′ ( x n ) ≠ 0 the next approximation is given by
There are k baskets and n balls. The balls are put into the baskets randomly. If k
Q. Sum and Difference Identities? Ans. These six sum and difference identities express trigonometric functions of (u ± v) as functions of u and v alone.
Taylor Series - Sequences and Series In the preceding section we started looking at writing down a power series presentation of a function. The difficulty with the approach
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