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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;
the base b of a triangle increases at the rate of 2cm per second, and height h decreases at the rate of 1/2 cm per second. Find rate of change of its area when the base and height
I have a question that hurts my head to work out. It is really confusing for me. It sais " By the start of the 21st century, only 1 in 6 babies in America was born with blue eyes.
tan45 degrees=tan(90degrees-45degrees)
The population of a city is observed as growing exponentially according to the function P(t) = P0 e kt , where the population doubled in the first 50 years. (a) Find k to three
Decision Trees And Sub Sequential Decisions A decision tree is a graphic diagram of different decision alternatives and the sequence of events like if they were branches of a t
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
test is tomorrow, don''t know anything lol, please help
(1) The following table gives the joint probability distribution p (X, Y) of random variables X and Y. Determine the following: (a) Do the entries of the table satisfy
weather prediction on monsoon past data on project
writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a
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