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Evalute : lim(ntooo)[(n)/(n^2+1^2)+(n)/(...

Evalute : `lim_(ntooo)[(n)/(n^2+1^2)+(n)/(n^2+2^2)+........+(1)/(2n)]`.

A

`(npi)/(4)`

B

`(pi)/(4)`

C

`(pi)/(4n)`

D

`(pi)/(2n)`

Text Solution

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The correct Answer is:
B
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CHHAYA PUBLICATION-QUESTION PAPER 2017-UNIT-3
  1. Let I=int(10)^(19)(sinx)/(1+x^8)dx. Then,

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  2. Let I1=int0^n[x]dx" and I2=int0^n{x}dx, where [x] and {x} are integral...

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  3. Evalute : lim(ntooo)[(n)/(n^2+1^2)+(n)/(n^2+2^2)+........+(1)/(2n)].

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  4. The value of the integral int0^1e^(x^2)dx

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  5. int0^(100)e^(x-[x])dx=

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  6. Solution of (x+y)^2(dy)/(dx)=a^2 ('a' being a constant ) is

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  7. The integrating factor of the first order differential equation x^2(x^...

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  8. If f(x)=int(-1)^x |t|dt, then for any xge0,f(x) is equal to

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  9. Let for all xgt0,f(x)=lim(nto oo)n(x^((1)/(n))-1), then

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  10. Let I=int0^(100pi)sqrt(1-cos2x)dx, then

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  11. The area (sq. units) of the figure bounded by the parabolas x= -2y^2" ...

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  12. Tangents are drawn to the ellipse (x^2)/(9)+(y^2)/(5)=1 at the ends of...

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  13. The value of K in order that f(x)=sinx-cosx-Kx+5 decreases for all pos...

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  14. For real x, the greatest value of (x^2+2x+4)/(2x^2+4x+9) is

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  15. Find solution of ydx+xdy=xy(dy-dx)

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  16. If f(x)=x^n,n being a non-negative integer, then the values of n for w...

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  17. Let f be a non-constant continuous function for all xge0. Let f satisf...

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  18. If the line ax+by+c=0,abne0, is a tangent to the curve xy=1-2x, then

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  19. Two particles move in the same straight line starting at the same mome...

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  20. If the tangents to y^2=4ax at the point (at^2,2at) where |t|>1 is a no...

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