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Evaluate the limit . underset(n to 00)...

Evaluate the limit .
`underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))………(1+(n^(2))/(n^(2)))]^(1/n)`

A

`e^((pi-4)//2)`

B

`2e^((pi-4)//2)`

C

`(e^((pi-4)//2))/(2)`

D

none

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DIPTI PUBLICATION ( AP EAMET)-DEFINITE INTEGRATION-EXERCISE 1D
  1. Lt(n-oo)[(1)/(n^(3))+(2^(2))/(n^(3))+.........+(n^(2))/(n^(3))]=

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

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

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

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

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

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

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

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  9. Lt(ntooo){(sqrt1+sqrt2+sqrt3+.........+sqrtn)/(nsqrtn)}

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

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

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  12. Lt(ntooo)[(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)-2^(2)))+(1)/(sqrt((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. Lt(ntooo)[(n^(1//2))/(n^(3//2))+(n^(1//2))/((n+3)^(3//2))+(n^(1//2))/(...

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  15. Lt(ntooo)(1)/(n){sin^(2)""(pi)/(2n)+sin^(2)""(2pi)/(2n)+..........+sin...

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  16. Lt(ntooo)(1)/(n)[sec^(2)""(pi)/(4n)+sec^(2)""(2pi)/(4n)+......+sec^(2)...

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  17. {:(" "Lt),(n rarr oo):} [ (1)/(n^(2)) sec^(2). (1)/(n^(2)) + (2)/(n^(2...

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  18. Evaluate underset(n to oo)("lim")[(1+(1)/(n))(1+2/n)* * * (1+(n)/(n))...

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  19. Evaluate the limit . underset(n to 00)("lim") [(1+(1)/(n^(2)))(1+(2^...

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  20. lim(ntooo)(((n+1)(n+2)....3n)/(n^(2n)))^(1//n) is equal to

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