Differential calculus, Mathematics

Assignment Help:

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}<=n

that 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;


Related Discussions:- Differential calculus

Limits, evaluate limit as x approaches 0 (x squared times sin (1/x)

evaluate limit as x approaches 0 (x squared times sin (1/x)

Theorem to computer the integral, Use green's theorem to computer the integ...

Use green's theorem to computer the integral F . dr where F = ( y^2 + x, y^2 + y) and c is bounded below the curve y= - cos(x),, above by y = sin(x) to the left by x=0 and to the r

Percents, write as a percent 6/10

write as a percent 6/10

Euler method for ode, y'' + 2y = 2 - e-4t, y(0) = 1 use euler''s method wit...

y'' + 2y = 2 - e-4t, y(0) = 1 use euler''s method with a step size of 0.2 to find and approximate values of y

Evaluate the following exponentials limit, Evaluate following limits. ...

Evaluate following limits. Solution: Let's begin this one off in the similar manner as the first part. Let's take the limit of each piece. This time note that since our l

Assumptions and application of t distribution, Assumptions and Application ...

Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 3.

Solution process of linear differential equations, For a first order linear...

For a first order linear differential equation the solution process is as given below: 1. Place the differential equation in the correct initial form, (1). 2. Determine the i

What is the median of her scores, Jody's English quiz scores are 56, 93, 72...

Jody's English quiz scores are 56, 93, 72, 89, and 87. What is the median of her scores? To find out the median, first put the numbers in sequence from least to greatest. 56, 7

Calculus, The law of cosines can only be applied to acute triangles. Is thi...

The law of cosines can only be applied to acute triangles. Is this true or false?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd