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Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(...

Evaluate `("lim")_(n rarr oo)sum_(k=1)^nk/(n^2+k^2)`

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CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

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  2. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

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  3. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

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  4. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

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  5. Show that : pi/6leint0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt2)

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  6. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

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  7. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

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  8. If alpha=int0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx where tan^-1x t...

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  9. Evaluate int(-4)^(-5)e^((x+5)^(2))dx+3int(1//3)^(2//3)e^(9(x-2/3)^(2))...

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  10. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

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  11. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/x

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  12. If for a real number y ,[y] is the greatest integral function less, th...

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  13. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/(1+x^2)

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  14. If int0^x {int0^u f(t) dt}du is equal to (a) int0^x (x-u) f(u) (b) ...

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  15. Compute the integrals: int(1/e)^e1/xsin(x-1/x)dx

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  16. STATEMENT 1: int0^pixsinxcos^2xdx=pi/2int0^pisinxcos^2x dx. STATEMEN...

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  17. Evaluate: int0^(pi/2)xcosx dx

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  18. Evaluate: int0^(pi/4)(sinx+cosx)/(9+16sin2x)dx

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  19. Evaluate: int(-pi//4)^(pi//4)log(sinx+cosx)dx

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  20. If alpha,beta(beta>alpha), are the roots of g(x)=a x^2+b x+c=0 and f...

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