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Lt(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+......

`Lt_(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=`

A

`1/2`

B

`1/3`

C

`2/3`

D

`3/2`

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-DEFINITE INTEGRALS-PRACTICE EXERCISE
  1. {:(" " Lt),(n rarroo):}1/n ((1)/(n+1) +(2)/(n+2)......+3/(4n))=

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  2. {:(" " Lt),(n rarroo):} [(1)/(3n+1)+(1)/(3n+2)+.......+(1)/(4n)]=

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  3. Lt(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=

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  4. {:(" " Lt),(n rarroo):} ((1+8+27+.......+n^(3))/(n^(4)))=

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  5. Lt(ntooo)(1^(9)+2^(9)+3^(9)+.........+n^(9))/(n^(10))=

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  6. Lt(n rarr oo)[(1^(99)+2^(99)+3^(99)+...+n^(99))/(n^(100))]

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  7. {:(" " Lt),(n rarroo):} [(1^(2))/(n^(3)+1^(3))+(2^(2))/(n^(3)+2^(3))+...

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  8. Lt(ntooo)[(1)/(1+n^(2))+(2)/(1+n^(2))+.............+(n)/(1+n^(2))]

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  9. {:(" " Lt),(n rarroo):} pi/n (sin. pi/n + sin. (2pi)/(n)+sin. (3pi)/(...

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  10. {:(" " Lt),(n rarroo):} (pi)/(2n) (1+ cos. (pi)/(2n)+....+cos. ((n-1)...

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  11. Evaluate the following define integrals as limit of sums : lim(n rar...

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  12. Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...

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  13. Lt(ntooo){(1)/(sqrt(n^(2)+1))+(1)/(sqrt(n^(2)+2^(2)))+.......+(1)/(sqr...

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  14. Evaluate the limit. underset(n to 00)("lim") (sqrt(n+1)+sqrt(n+2)+…...

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  15. Evaluate the following define integrals as limit of sums : lim(n rar...

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  16. int(r//6)^(pi//4)(dx)/(sin2x)=

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  17. int(1//pi)^(2//pi)(sin(1//x))/(x^(2))dx=

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  18. int(0)^(1)(4x^(3))/(sqrt(1-x^(8)))dx=

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  19. int(0)^(1) (1)/(sqrt(2+3x))dx=

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  20. int(0)^(1)(1-x)/(1+x)dx=

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