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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;
A farmer has a rectangular field of length 100m and breadth 70m. He leaves a path of 1m all along the boundary inside it. He decides to apply a manure to the remaining part of the
2x+3y=1, 5x+7y=3.
How to conversion into metric
Marty used the subsequent mathematical statement to show he could change an expression and still get the similar answer on both sides: 10 × (6 × 5) = (10 × 6) × 5 Which mathematica
Area with Polar Coordinates In this part we are going to look at areas enclosed via polar curves. Note also that we said "enclosed by" in place of "under" as we usually have
Sin129
applications of composit functions
Describe the System with 3 Variables ? This is an example of solving a system of equations using the substitution method. Warning: You will not understand this example if you
We have seen that if y is a function of x, then for each given value of x, we can determine uniquely the value of y as per the functional relationship. For some f
Two trains were traveling in opposite directions, moving away from one another. One train was moving at 5 miles per hour. The other train was moving at 6 miles per hour. They were
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