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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;
Derivative and Differentiation The process of acquiring the derivative of a function or slope or gradient is referred to as differentiation or derivation. The derivative is de
Calculus with Vector Functions In this part we need to talk concisely on derivatives, limits and integrals of vector functions. Like you will see, these behave in a quite pred
Survey 83% of community for a park. Randomly select 21 people if they do or do not want a park. Can you use normal distribution to approximate binomial distribution?If so find mean
x^2-5x+4 can written in roots as (x-1)*(x-4) x^2-4 can be written interms of (x-2)(x+2).so [(x-1)(x-4)/(x-2)(x+2)]
Determine that in a Boolean algebra, for any a and b, (a Λ b) V (a Λ b' ) = a. Ans: This can be proved either by using the distributive property of join over meet (or of mee
write the value of the 3 in each number
Testing the hypothesis equality of two variances The test for equality of two population variances is based upon the variances in two independently chosen random samples drawn
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if x+y+z=pi=180 prove that sin^2x+sin^2y+sin^z-2sinx*siny*sinz=2
Related problems,working rule,defnitions
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