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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;
maximize Z=2x+5y+7z, subject to constraints : 3x+2y+4z =0
Two angles are complementary. The larger angle is 15° more than twice the smaller. Find out the measure of the smaller angle. Let x = the number of degrees in the smaller angle
Three Dimensional geometry Intorduction In earlier classes we studied about the coordinates in two planes that is the XY plane. Here we are going to study in detail about th
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Q. Show Trigonometric Functions on a Graph? Ans. By discussing the trig functions with respect to an angle in a right-angle triangle, we have only considered angles betwee
A recipe calls for 2 1/4 teaspoons of salt for every 1 1/8 teaspoons of black pepper used. How many teaspoons of salt are needed for each teaspoon of pepper used ?
3.6 in a fraction
how do you round to the nearest dollars?
Ratio of successes in 5 independent trials to the probability of successes in two independent trials is 1/4. What is the probability of 4 successes in 6 independent trials?
use 3/8 of a thin of paint, what fraction of the paint is left in thin (show work
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