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The value of lim(n->oo) [(1+1/n^2)(1+2^2...

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

A

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

B

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

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If int(0)^(x^(2)) sqrt(1=t^(2)) dt, then f'(x)n equals

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  2. The value of integral int(1)^(e) (log x)^(3)dx , is

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  3. If int(x^(2))^(x^(4)) sin sqrt(t) dt, f'(x) equals

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  4. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  5. The value of lim(n->oo) [(1+1/n^2)(1+2^2/n^2)...(1+n^2/n^2)]^(1/n)

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  6. If int(0)^(1) e^(x^(2))(x-alpha)dx=0 then

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  7. If f(x) satisfies the requirements of Rolle's Theorem in [1,2] and f(x...

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  8. The value of the integral int(0)^(1) cot^(-1) (1-x+x^(2))dx, is

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  9. The integral int(-1)^(1) (|x+2|)/(x+2)dx is equal to

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  10. Let I= int(0)^(1) (x^(x))/( x+1) dx, then the vlaue of the intergral ...

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  11. The value of the integral int(0)^(pi) (xdx)/(1+cos alpha sinx), 0 lt a...

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  12. int(pi)^(10n) |sin x|dx is equla to

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  13. If int0^pi 1/(a+bcosx)dx=pi/sqrt(a^2-b^2), then int0^pi 1/(a+bcosx)^2d...

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  14. If int(1)^(oo) e^(-ax) dx=(1)/(a),"then" int(1)^(oo) x^(n)e^(-ax)dx...

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  15. The value of int(pi)^(2pi) [ 2 sin x] dx, where [] repreents the great...

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  16. If f(x)=Asin((pix)/2)+B, f'(1/2)=sqrt2 and int0^1 f(x)dx=(2A)/pi then ...

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  17. If I(m,n)= int(0)^(1) x^(m) (ln x)^(n)dx then I(m,n) is also equal to

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  18. lim(n->oo)(1^(99)+2^(99)+3^(99)+.......n^(99))/(n^(100))=

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  19. If I(n)=int(0)^(pi//4) tan^(n) x dx, lim(n to oo) n(I(n+1)+I(n-1)) equ...

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  20. int(0)^(a) f(x) dx= lambda and int(0)^(a) f(2a-x) dx= mu, then int(0)^...

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