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lim(n rarr oo)[(e^(1//n)+e^(2//n)+e^(3//...

`lim_(n rarr oo)[(e^(1//n)+e^(2//n)+e^(3//n)+...+e^(n //n))/n]`

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A DAS GUPTA-Definite Integration-EXERCISE
  1. Evaluate lim(nrarroo)(2)/(n)(sin.(pi)/(2n)+sin.(2pi)/(2n)+sin.(3pi)/...

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  2. underset(ntoinfty)lim(n/(n^2+1^2)+n/(n^2+2^2)+n/(n^2+3^2)+...+1/(2n)) ...

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

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  4. lim(nrarroo)((1)/(sqrt(n^(2)))+(1)/(sqrt(n^(2)-1^(2)))+(1)/(sqrt(n^(2)...

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  5. underset(nto oo)lim{(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+...+(1)/(n+n)} is, e...

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  6. lim(n->oo)1/n[1/(n+1)+2/(n+2)+....+(3 n)/(4 n)]

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  7. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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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. Evaluate intcos^5(x/2)sinxdx

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  10. Evaluate the following:int0^(pi/2)(sinxcosxdx)/((a^2cos^2x+b^2sin^2x)^...

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  11. Evaluate int0^(pi//2)(sin^2xdotcos^2x)/((sin^3x+cos^3x)^2)dx

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  12. Evaluate the following:int0^1xlogxdx

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  13. Evaluate : int1^16tan^(- 1)sqrt(sqrt(x)-1)dx

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  14. Evaluate the following integrals: int(cosx)/(cos(x+alpha))dx

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  15. Evaluate the following:int0^1(x^3dx)/(1+x^4)

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  16. int0^1(x dx)/(sqrt(x+lambda)+sqrt(x+mu)),lambda!=mu

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  17. By using the properties of definite integrals, evaluate the integra...

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  18. int0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

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  19. Evaluate the following : int(pi//2)^(pi)e^(x)((1-sinx)/(1-cosx))dx.

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  20. integrate int0^(2pi) e^x . sin (pi/4 + x/2) dx

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