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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;
sin2A+cos2A
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Velocity Problem : Let's look briefly at the velocity problem. Several calculus books will treat it as its own problem. . In this problem we are given a position function of an
we know that derivative of x 2 =2x. now we can write x 2 as x+x+x....(x times) then if we take defferentiation we get 1+1+1+.....(x times) now adding we get x . then which is wro
Ask questioOn average, Josh makes three word-processing errors per page on the first draft of his reports for work. What is the probability that on the next page he will make a) 5
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Ask queFind the normalized differential equation which has {x, xex} as its fundamental setstion #Minimum 100 words accepted#
All differential equations will doesn't have solutions thus it's useful to identify ahead of time if there is a solution or not. Why waste our time trying to get something that doe
What is Geometry?
If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans: d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,
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