value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Rounding, how do you round to the nearest dollars?

how do you round to the nearest dollars?

Vector arithmetic - addition, Vector Arithmetic In this part we need t...

Vector Arithmetic In this part we need to have a brief discussion of vector arithmetic. Addition We will begin with addition of two vectors. Thus, given the vectors a

Two consecutive positive integers whose product is 90, What is the lesser o...

What is the lesser of two consecutive positive integers whose product is 90? Let x = the lesser integer and let x + 1 = the greater integer. Because product is a key word for m

Operation research, Advantages and disadvantages of operation researchs

Advantages and disadvantages of operation researchs

School mathematics, I am interested in school mathematics online assignment...

I am interested in school mathematics online assignments , homework help, projects etc. I have good knowledge of mathematics and experience of 15+ years teaching mathematics in cen

Making equally sized groups-prerequisites for multiplication, Making Equall...

Making Equally Sized Groups :  By the time children reach Class 1 or 2, they would have had many experiences of pairs of objects-pairs of shoes, pairs of eyes, ears, arms, legs, w

Assemble the coefficient matrix and solve the linear system, Solve discrete...

Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length

Mr, i needed help with algebra

i needed help with algebra

Properties of radicals, If n is positive integer greater than 1 and a & b b...

If n is positive integer greater than 1 and a & b both are positive real numbers then, Consider that on occasion we can let a or b to be negative and yet have these propert

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