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Evaluate lim ( x to oo) ((1^(2) )/(n ^(...

Evaluate `lim _( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +2 ^(3)) + (3 ^(2))/(n ^(3)+ 3 ^(3))+ .... + (4)/(9n)).`

A

`1/3 ln 3`

B

`(ln 9)/(3)`

C

`(ln 4)/(3)`

D

`(ln 6)/(3)`

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The correct Answer is:
A
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lim_ (n rarr oo) [(1 ^ (2)) / (n ^ (3) + 1 ^ (3)) + (2 ^ (2)) / (n ^ (3) + 2 ^ (3)) + (3 ^ (2)) / (n ^ (3) + 3 ^ (3)) + ... * (1) / (2n)]

Prove that lim_ (n rarr oo) ((1 ^ (2)) / (n ^ (3)) + (2 ^ (2)) / (n ^ (3)) + (3 ^ (2)) / ( n ^ (3)) + .... + (n ^ (2)) / (n ^ (3))) = (1) / (3)

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

The value of lim_(n to oo)((1)/(1^(3)+n^(3))+(2^(2))/(2^(3)+n^(3))+..........+(n^(2))/(n^(3)+n^(3))) is :

lim_ (n rarr oo) [(1) / (n) + (n ^ (2)) / ((n + 1) ^ (3)) + (n ^ (2)) / ((n + 2) ^ (3)) + ...... + (1) / (8n)]

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

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lim_ (n rarr oo) [(1 ^ (3)) / (n ^ (4) + 1 ^ (4)) + (2 ^ (3)) / (n ^ (4) + 2 ^ (4)) ++ (1) / (2n)] =

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VK JAISWAL-INDEFINITE AND DEFINITE INTEGRATION-EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Evaluate lim ( x to oo) ((1^(2) )/(n ^(3) +1 ^(3))+(2 ^(2))/(n ^(3) +...

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  2. int (x+ ( cos^(-1)3x )^(2))/(sqrt(1-9x ^(2)))dx = (1)/(k (1)) ( sqrt(1...

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  3. If int (0)^(oo) (x ^(3))/((a ^(2)+ x ^(2)))dx = (1)/(ka ^(6)), then fi...

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  4. int( (x^2+1)dx)/x

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  5. If int (x ^(6) +x ^(4)+x^(2)) sqrt(2x ^(4) +3x ^(2)+6) dx = ((ax ^(6) ...

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  6. int( x^2+3)/(x^2+2)dx

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  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  8. Let int (0)^(1) (4x ^(3) (1+(x ^(4)) ^(2010)))/((1+x^(4))^(2012))dx = ...

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  9. Let int ( 1) ^(sqrt5)(x ^(2x ^(2)+1) +ln "("x ^(2x ^(2x ^(2+1)))")")dx...

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  10. If int (dx )/(cos ^(3) x-sin ^(3))=A tan ^(-1) (f (x)) +bln |(sqrt2+f ...

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  11. Find the value of |a| for which the area of triangle included between ...

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  12. Let I = int (0) ^(pi) x ^(6) (pi-x) ^(8)dx, then (pi ^(15))/((""^(15) ...

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  13. int( x^3)/(x^2-3)dx

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  14. If a continuous function f on [0,a] satisfies f(x)f(a-x)=1,agt0, then ...

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  15. If {x} denotes the fractional part of x, then I = int (0) ^(100) (sqrt...

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  16. int( x^3)/(x^2-2)dx

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  17. IF M be the maximum valur of 72 int (0) ^(y) sqrt(x ^(4) +(y-y^(2))^(2...

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  18. Find the number points where f (theta) = int (-1)^(1) (sin theta dx )/...

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  19. underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)...

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  20. The maximum value of int (-pi//2) ^(2pi//2) sin x. f (x) dx, subject t...

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  21. Given a funtion g, continous everywhere such that g (1)=5 and int (0)^...

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