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How calculate limit of string if i don't know calculate integral? string u=n^4*integral...
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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.
Use`nltc_nltn+1` => `lim_(n->oo)``c_n=oo`
`` 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.
Posted by sciencesolve on November 24, 2011 at 5:25 AM (Answer #1)
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