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lim(n rarr oo) { n/(n^(2)+1^(2)) + n/(n^...

`lim_(n rarr oo) { n/(n^(2)+1^(2)) + n/(n^(2)+2^(2))+......+ n/(n^(2)+n^(2))}` is equal to

A

1

B

0

C

`pi/4`

D

`pi/2`

Text Solution

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The correct Answer is:
C
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
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  3. lim(n rarr oo) { n/(n^(2)+1^(2)) + n/(n^(2)+2^(2))+......+ n/(n^(2)+n^...

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  4. The value of the integral int0^(pi/4) (sin theta + cos theta)/(9+16 si...

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  7. For any integer n, the integral : int0^(pi) e^(cos^2) cos^(3) (2n + 1)...

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  8. If g(x) = int0^x cos^4 t dt, then g(x + pi) equals:

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  9. If I(n) = int0^(pi/4) tan^(n) theta d theta, then I(8)+I(6) equals

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  10. The value of int0^(pi/2) (1)/(1+tan^(3)x) dx is

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  11. Let f : R to R and g : R to R be continuous functions. Then the value ...

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  12. If f(a + b - x) = fx, then inta^b x f(x) dx is equal to :

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  13. int0^(pi/2) (dx)/(1+cotx) =

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  14. If f and g are continuous [0,a) satisfying f(x) = f(a-x) and g(x)+ g(a...

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  16. int0^(10) |x(x-1)(x-2)| dx is equal to

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  17. If I = int0^(pi/4) log (1+ tan x) dx, then I =

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  18. lim(n rarr oo) {1/n+1/(n+1)+1/(n+2)+…..+1/(3n)} =

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  19. If I = int(-pi)^(pi) (e^(sinx))/(e^(sinx)-e^(-sinx)) dx then I =

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  20. lim(x rarr oo) (int(0)^(2x) xe^(2)dx)/(e^(4x^(2))) equals :

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