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lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+...

`lim_(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n/(n+3(n-1)))]=`

A

`2sqrt(2)`

B

`2(sqrt(2)-1)`

C

`2`

D

`4`

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-DEFINITE INTEGRALS-EVALUATIO TEST
  1. Prove that int(a)^(b)f(x)dx=(b-a)int(0)^(1)f((b-a)x+a)dx

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  2. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

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  3. If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x...

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  4. lim(ntooo)1/n[1+sqrt(n/(n+1))+sqrt(n/(n+2))+sqrt(n/(n+3))+………..+sqrt(n...

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  5. lim(n->oo)sum(n=1)^n(sqrt(n))/(sqrt(r)(3sqrt(r)+4sqrt(n))^2)

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  6. Let f(x) be a function satisfyingf'(x)=f(x) withf(0) =1 and g(x) be a ...

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  7. int(0)^(100pi)(|sin^(3)x|+|cos^(3)x|)dx=

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  8. I1=int0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I2=int0^(2pi)cos^6xdx ,I3=in...

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  9. overset(2pi) underset(0)int(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0...

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  10. The equation int(-pi/4)^(pi/4){a|sinx|+(bsinx)/(1+cos^2x)+c}dx=0 where...

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  11. int(0)^(sqrt("log"(pi)/2))cos(e^(x^(2)))2xe^(x^(2))dx=

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  12. If f(x)=int(0)^(x)sin^(6)tdt, then f(x+pi)=

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  13. If f(x) is a polynomial of degree 2, such that f(0)=3,f'(0)=-7,f''(0)=...

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

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  15. If f(x)=|(sin x+sin x 2x+sin3x,sin2x,sin3x),(3+4sinx,3,4sinx),(1+sinx,...

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  16. If a is a positive integer, then the number of values of a satisfying ...

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  17. If for all real numbers y ,[y] is the greatest integer less than or eq...

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  18. Let f(x) = |{:(secx,cosx,sec^(2)x+cotx cosecx),(cos^(2)x,cos^(2)x,cose...

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  19. If (1)/(sqrt(a))underset(1)overset(a)int((3)/(2)sqrt(x)+1-(1)/(sqrt(x)...

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  20. Let d/(dx)F(x)=((e^(sinx))/x),x > 0. If int1^4 3/x e^s in x^3dx=F(k)-...

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