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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;
Distinguish between Mealy and Moore Machine? Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.on..
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1/sec A+tan A =1-sin A /cos A
Implicit Differentiation : To this instance we've done quite a few derivatives, however they have all been derivatives of function of the form y = f ( x ) . Unluckily not all
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First, larger the number (ignoring any minus signs) the steeper the line. Thus, we can use the slope to tell us something regarding just how steep a line is. Next, if the slope
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