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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

`2e^(pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
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  2. Let I = int(1)^(3)sqrt(x^(4)+x^(2)), dx then

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  3. I=int0^(2pi) e^(sin^2x+sinx+1)dx then

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  4. Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to

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  5. Let mean value of f(x) = 1/(x+c) over interval (0,2) is 1/2 ln 3 then...

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  6. lim(nrarr0) sum(r=1)^(n) ((r^(3))/(r^(4)+n^(4))) equals to :

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

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  8. 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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  9. lim(nrarroo) [sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))/(n)pi] i...

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  10. Let I(n) = int(0)^(1)(1-x^(3))^(n)dx, (nin N) then

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  11. The area bounded by the x-axis and the curve y = 4x - x^2 - 3 is

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  12. The area of the figure bounded by right of the line y = x + 1, y= cos ...

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  13. Area bounded by curve y^(3) - 9y + x = 0, and y-axis is

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  14. Let f":[0,oo)rarr R be a continuous and stricity increasing function ...

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  15. Find the area bounded by the curves y = e^(x), y = |x-1| and x = 2.

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  16. The area bounded by y = 2-|2-x| and y=3/|x| is:

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  17. The area bounded by the curve y^(2) = 4x and the line 2x-3y+4=0 is

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  18. Area of region bounded by x=0, y=0, x=2, y=2, y<=e^x & y>=lnx is

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  19. The area between the arms of the curve |y|=x^(3) from x = 0 to x = 2 i...

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  20. The area bounded by the parabolas y=(x+1)^2 and y=(x-1)^2a n dy=(x-1)^...

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