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lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))...

`lim_(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+....+(1)/(2n))`

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Evaluate: lim_(n rarr oo)((1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(4))+...+(1)/(n))

lim_(n rarr oo)[(1^(2))/(n^(3))+(2^(2))/(n^(3))+(3^(2))/(n^(3))+...+(n^(2))/(n^(3))]=?

lim_(n rarr oo)(1)/(n^(4))sum_(r=1)^(n)r^(3)=

lim_ (n rarr oo) ((1) / (3) + (1) / (3 ^ (2)) + (1) / (3 ^ (3)) ++ (1) / (3 ^ (n) ))

lim_(n to oo) [ 1^2/n^3 + (2^2)/(n^3) + …+ ((n-1)^2)/(n^3)]

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

lim_(n rarr oo)(((n+1)^(1/3))/(n^(4/3))+((n+2)^(1/3))/(n^(4/3))+.....+((2n)^(1/3))/(n^(4/3))) is equal to

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

A DAS GUPTA-Definite Integration-EXERCISE
  1. Evaluate the following integrals as limit of sum: inta^b e^x dx

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  2. Integrate int1^2x^3dx

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  3. lim(n to oo)((1)/(1+n^(3))+(4)/(8+n^(3))+....+(r^(2))/(r^(3)+n^(3))+.....

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  4. Evaluate lim(nrarroo)(2)/(n)(sin.(pi)/(2n)+sin.(2pi)/(2n)+sin.(3pi)/...

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

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

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

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

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

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

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  11. 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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  12. Evaluate intcos^5(x/2)sinxdx

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

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

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  15. Evaluate the following:int0^1xlogxdx

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

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

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

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

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

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