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Find the limit, when n->oo,\ of\ [((n^...

Find the limit, when `n->oo,\ of\ [((n^3+1^3)(n^3+2^3)(n^3+3^3)........(n^3+n^3))/(n^(3n))]^(1/n)`

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lim_(n -> oo) (((n+1)(n+2)(n+3).......3n) / n^(2n))^(1/n)is equal to

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

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 :

1.3+2.3^(2)+3.3^(3)+............+n.3^(n)=((2n-1)3^(n+1)+3 )/(4)

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

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

1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)

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)).

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

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  11. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

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

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  13. Let f(x)=\ int1^xsqrt(2-t^2)dtdot Then the real roots of the equati...

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  14. Let T >0 be a fixed real number. Suppose f is continuous function su...

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  15. The tangent int(-1/2)^(1/2)([x]+ln((1+x)/(1-x)))\ dx equals, where [\ ...

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  16. int0^pisqrt((1-x)/(1+x))dx= (pi^)/2 (b) (pi^)/2-1 (c) (pi^)/2+1...

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  17. If f(x) is differentiable and int0^(t^2)xf(x)dx=2/5t^5, then f(4/(25))...

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  18. If y(x)=\ int(pi^2//16)^(x^2)(cos xdotcossqrt(theta))/(1+sin^2sqrt(the...

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  19. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|pi/3))dx

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  20. If int(sinx)^1 t^2f(t)dt=1-sinx, then the value of f(1/sqrt(3)) is (A)...

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