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lim(n rarr oo) 1/2 [(n+1)(n+2)…….2n]^(1/...

`lim_(n rarr oo) 1/2 [(n+1)(n+2)…….2n]^(1/n) =`

A

4/e

B

2/e

C

1/e

D

e

Text Solution

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The correct Answer is:
A
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HIMALAYA PUBLICATION-Definite Integrals and its Application-QUESTION BANK
  1. The value of int0^(1) tan^(-1) ((2x-1)/(1+x-x^(2))) dx is

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  2. lim(n rarr oo) sum(r=1)^(n) r/n^(2) sec^(2) (r^(2)/n^(2)) =

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  3. lim(n rarr oo) 1/2 [(n+1)(n+2)…….2n]^(1/n) =

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  4. lim(n rarr oo)[(1+1/n)(1+2/n)…..2]^(1/n) =

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  5. lim(n rarr oo) 1/n^(100) (1^(99)+2^(99)+3^(99)+………+n^(99)) =

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  6. lim(n to oo) sum(r = 1)^(n) 1/n e^(r/n) is :

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  7. lim(n rarr oo) sum(r=1)^(n) 1/n sec^(2) ((rpi)/(4n)) =

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  8. lim(n rarr oo)1/nsum(r=1)^(n) sqrt(r/n) =

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  9. lim(n rarr oo) 1/n[sin(pi/(2n))+sin(pi/n)+sin((3pi)/2n)+........+sin(p...

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  10. The area between the curves y=2x-x^(2) and the x-axis is

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  11. The area bounded by the curve y = x^2 - 7x + 10 and the x - axis is

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  12. The area bounded byy^(2) =x^(3), the y-axis and the lines y=1 and y=2 ...

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  13. The area bounded by y=sin x and x-axis from x=0 to x=pi is

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  14. The area bounded by y=sin x and x-axis from x=0 to x=pi is

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  15. Area under the curve y= sin 2x + cos 2x between the ordinates x=0 and ...

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  16. The area enclosed by the curve y=sin^(3)x between x=0 and x=pi/2

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  17. The area of the figure bounded by the curves y=cosx and y=sinx and the...

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  18. The area bounded by the parabola y^(2) = 4x and x^2 = 4y is

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  19. Area of the region bounded by y^(2) = 8x and the latus rectum is

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  20. Area bounded by the barabola y^(2) = 8x and the line y=3x is

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