Homework Help

How calculate limit of string if i don't know calculate integral? string u=n^4*integral...

user profile pic

rouche | Student, Undergraduate | (Level 1) Honors

Posted November 23, 2011 at 5:41 PM via web

dislike 0 like

How calculate limit of string if i don't know calculate integral?

string u=n^4*integral x/1+x^5

integral is definite in [n,n+1]

class tutor said that i need not to know integrals

1 Answer | Add Yours

Top Answer

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted November 24, 2011 at 5:25 AM (Answer #1)

dislike 2 like

The Mean Value Theorem helps you to solve the problem.

The function under the definite integral is a continuous function, therefore the Mean Value Theorem is applicable.

`int_a^bf(x)dx=(b-a)*f(c)` , c`in` [a,b]

In this case, the string=`n^4` *`int_n^(n+1)x/(1+x^5)dx` `=n^4*(n+1-n)*f(c_n)=n^4*f(c_n)`

Use the notation `u_n`  for the string.

`u_n=n^4*c_n/(1+(c_n)^5)`

`u_n=(n/c_n)^4*(c_n)^5/(1+(c_n)^5)`

Use`nltc_nltn+1`  => `lim_(n->oo)``c_n=oo`

`1/ngt1/c_ngt1/(n+1)`

`` Multiply by n>0 =>

`n/ngtn/c_ngtn/(n+1)=gt1gtn/cgtn/(n+1)` =>`lim_(n->oo)` `(n/c_n)=1`

ANSWER: The limit of string is 1.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes