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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;
X-intercept If an intercept crosses the x-axis we will call it as x-intercept . Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Example 1 Add 4x 4 + 3x 3 - x 2 + x + 6 and -7x 4 - 3x 3 + 8x 2 + 8x - 4 We write them one below the other as shown below.
Memphis, Tennessee, and New Orleans, Louisiana, lie approximately on the same meridian. Memphis has latitude 35°N and New Orleans has latitude 30°N. Find the distance between these
What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or
Reduction -when the original amount and the balance or remainder are known, to find the part that has been given away. (e.g., there were 15 toffees in a container, and there are
The subsequent force that we want to consider is damping. This force may or may not be there for any specified problem. Dampers work to counteract any movement. There are some w
Probability Distribution for Continuous Random Variables In a continuous distribution, the variable can take any value within a specified range, e.g. 2.21 or 1.64 compared to
The Hurwiz method Hurwiz method was the concept of coefficient of optimism or pessimism introduced by L. Hurwicz. The decision maker takes into account both the minimum and max
what are core concepts of marketing?
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