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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;
Which of the subsequent decimals is the greatest number? If you add zeros to the end of every of the numbers so that each number has 5 places after the decimal point, it is sim
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Evaluate the given limits, showing all working: Using first principles (i.e. the method used in Example 1, Washington 2009, Using definition to find derivative ) find the
factories Y=(B+CA)(C+A''B)
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