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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;
Michael made 19 out of 30 free-throws this basketball season. Larry's freethrow average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-th
Example of Integrals Involving Trig Functions Example: Estimate the following integral. ∫ sin 5 x dx Solution This integral no longer contains the cosine in it that
solving
Time Series Models Additive Model Time series value = T +S +C +R Whereas S, C and R are expressed in absolute value Additive Model model is best suited where the
The owner of TMH Hospital wants to open a new facility in a certain area. He usually builds 25-, 50-, or 100-bed facilities, depending on whether anticipated demand is low, medium
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For the layman, a "function" indicates a relationship among objects. A function provides a model to describe a system. Economists refer to deman
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Find the probability of having 53 Sundays in (i) a leap year (ii) a non leap year (Ans:2/7 , 1/7 ) Ans: An ordinary year has 365 da
Finite Population Correction Factor Or Fpcf) If a specified population is relatively of small size and sample size is more than 5 percent of the population then the standard er
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