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Lt(ntooo)sum(r=0)^(n-1)(n)/(n^(2)+r^(2))...

`Lt_(ntooo)sum_(r=0)^(n-1)(n)/(n^(2)+r^(2))=`

A

1

B

`pi`

C

`pi//2`

D

`pi//4`

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DIPTI PUBLICATION ( AP EAMET)-DEFINITE INTEGRATION-EXERCISE 1D
  1. Lt(ntooo)sum(r=0)^(n-1)(n)/(n^(2)+r^(2))=

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  2. Lt(ntooo)sum(r=1)^(n)(1)/(sqrt(4n^(2)-r^(2)))=

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  3. Lt(ntooo)sum(r=1)^(n-1)(1)/(sqrt(n^(2)-r^(2)))=

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  4. Lt(ntooo)(1)/(n)sum(r=1)^(2n)(r)/(sqrt(n^(2)+r^(2)))=

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  5. Lt(ntooo)sum(r=1)^(n)(1)/(n)[sqrt ((n+r)/(n-r))]

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  6. Lt(ntooo){(1)/(n+1)+(1)/(n+2)+......+(1)/(2n)}=

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  7. Lt(ntooo)sum(r=0)^(n-1)(1)/(n+r)=

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  8. Lt(ntooo){(1)/(n)+(1)/(n+1)+(1)/(n+2)+.......+(1)/(3n)}=

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  9. Lt(ntooo){(1)/(2n+1)+(1)/(2n+2)+(1)/(2n+3)+..........+(1)/(2n+n)}=

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  10. Lt(ntooo)[(1)/(3n+1)+(1)/(3n+2)+............+(1)/(3n+n)]=

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  11. Lt(ntooo)[(1)/(1-n^(2))+(2)/(1-n^(2))+.......+(n)/(1-n^(2))]=

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  12. Lt(ntooo){(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+.......+1/(n)}

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

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  14. Lt(ntooo)([1+4+9+......+n^(2)])/(n^(3))

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

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  16. Evaluate the limit . underset(n to 00)("Lt") (1+2^(4)+3^(4)+…….+n^(4...

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  17. Lt(ntooo)sum(r=1)^(n)(1)/(n)e^(r//pi) is

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  18. Lt(ntooo)[(1)/(1+n^(3))+(4)/(8+n^(3))+(9)/(27+n^(3))+.......+(1)/(2n)]...

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  19. Lt(ntooo)[(1^(3))/(n^(4)+1^(4))+(2^(3))/(n^(4)+2^(4))+.........+(1)/(2...

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  20. By the definition of the definite integral, the value of lim(ntooo)((...

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