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The value of lim(n to oo)[(n)/(n^(2))+(n...

The value of `lim_(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+...+(n)/(n^(2)+(n-1)^(2))]` is :

A

`(pi)/(2)`

B

`(pi)/(4)`

C

`pi`

D

`-(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
B
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VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -Level - 1
  1. Evaluate : lim(n to oo)[(sqrt(n))/((3+4sqrt(n))^(2))+(sqrt(n))/(sqrt(2...

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  2. lim(n->oo)[1/sqrt(2n-1^2) +1/sqrt(4n-2^2)+1/sqrt(6n-3^2)+...+1/n]

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  3. The value of lim(n to oo)[(n)/(n^(2))+(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(...

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  4. lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....

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  5. lim(n to oo)[(n+1)/(n^(2)+1^(2))+(n+2)/(n^(2)+2^(2))+....+(1)/(n)]

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  6. underset(nrarroo)("lim")[(1+(1)/(n^(2)))(1+(2^(2))/(n^(2)))"....."(1+(...

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  7. lim(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

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  8. IfSn=[1/(1+sqrt(n))+1/(2+sqrt(2n))++1/(n+sqrt(n^2))],t h e n(lim)(n ra...

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  9. The value of lim(n to oo)sum(r=1)^(n)(1)/(n) sqrt(((n+r)/(n-r))) is :

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  10. The value of lim(n->oo)(sqrt(1)+sqrt(2)+sqrt(3)+.....+sqrt(n))/(nsqrt(...

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  11. Evaluate: ("lim")(nvecoo)[1/(n^2)sec^2 1/(n^2)+2//n^2sec^2 4/(n^2)++1/...

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  12. lim(n to oo)(1)/(n)[tan.(pi)/(4n)+tan.(2pi)/(4n)+…..+tan.(n pi)/(4n)]

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  13. If (d)/(dx)f(x)=g(x) for a le x le b then, overset(b)underset(a)int f...

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  14. If underset(1)overset(x)int(dt)/(|t|sqrt(t^(2)-t)) = (pi)/(6), then x ...

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  15. Iff(x)=e^(g(x))a n dg(x)=int2^x(tdt)/(1+t^4), then find the value of ...

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  16. If x=int(0)^(y)(dt)/(sqrt(1+9t^(2)))and (d^(2)y)/(dx^(2))=a^(2)y then ...

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  17. f(x)=int0^x f(t) dt=x+intx^1 tf(t)dt, then the value of f(1) is

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  18. If f(x)=cosx-int0^x(x-t)f(t)dt ,t h e nf^(prime)(x)+f(x) is equal to -...

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  19. If f(-x)+f(x)=0 then inta^x f(t) dt is

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  20. If int0^af(2a-x)dx=m and int0^af(x)dx=n, then int0^(2a) f(x) dx is equ...

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