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lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /...

`lim_(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)`

A

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

B

` 2e ^(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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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. underset(n to oo)"lim"underset(r=1)overset(n)sum((r^(3))/(r^(4) + n^(4...

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  2. underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-...

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

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  4. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  5. Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+...

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  6. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

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  7. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  8. Let I (1) = int (1) ^(2) (dx )/(sqrt(1 + x ^(2))) and I (2) = int (1) ...

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  9. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  10. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

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  11. If u (n) = int (0) ^(pi//2) x ^(n) sin x dx, n in N then the value of ...

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  12. The vlaue of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  13. In = int0^(pi/4) tan^n x dx , then the value of n(l(n-1) + I(n+1)) is

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  14. The value of the integral l = int(0)^(1) x(1-x)^(n) dx is

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  15. Let I (1) = int (0) ^(1) (e ^(x) dx )/( 1 + x) and I (2) = int (0) ^(1...

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  16. If f(x) is a function satisfying f(1/x)+x^2f(x)=0 for all nonzero x , ...

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  17. If underset(0)overset(100)intf(x) dx = a, then underset(r=1)overset(10...

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  18. If f(x) and g(x) are continuous functions, then int(In lamda)^(In (1//...

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  19. underset(2-ln3)overset(3+ln3)int(ln(4+x))/(ln(4+x)+ln(9-x))dx is equal...

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  20. If [x] stands for the greatest integer function, the value of overset(...

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