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Evaluate lim(n->oo)[1^2/(n^3+1^3) + 2^...

Evaluate
`lim_(n->oo)[1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3)+…+1/(2n)]`

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UNITED BOOK HOUSE-HIGHER SECONDARY QUESTION 2018-EXERCISE
  1. A relation R is defined on the set of natural numbers N as follows: R=...

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  2. answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...

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  3. (b) answer the foll. Questions: (i) express the matrix A=[[3,2,3],[4,5...

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  4. if |[x-1,1,1],[1,x+1,-1],[-1,1,x+1]| =0 , find the value of x.

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  5. answer the foll. Questions: (i) if y=(sin^(-1)x)/(sqrt(1-x^2)) , then ...

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  6. or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...

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  7. answer the foll. Questions: (ii)evaluate :int (x^4+1)/(x^6+1) dx

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  8. or, evaluate :int dx/(cos x+sqrt 3 sin x)

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  9. answer the foll. Question: (iii) solve : x dy/dx = y+x tan (y/x) , giv...

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  10. or , solve:(1-x^2) dy/dx - xy=1 .

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  11. (d) answer any one question : (i) if three vectors vec a, vec b and ve...

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  12. answer any one question : (ii) let vec a= hat i+4 hat j+ 2hat k , vec...

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  13. Evaluate lim(n->oo)[1^2/(n^3+1^3) + 2^2/(n^3+2^3) +3^2/(n^3+3^3)+…+1...

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  14. answer any one question : (ii) evaluate : int0^pi (x sin x)/(1+cos ^2x...

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  15. answer any one question : (ii) if X and Y are two independent variable...

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  16. (b)answer any two questions : (i) a circular ink blot grows at the rat...

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  17. answer any two questions :(iii) if the straight line lx+my=n be a norm...

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  18. answer any two questions :(iv) solve :(2x-10y^3) dy/dx+y=0 .

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  19. ©answer any one question: (i) find the vector equation of the plane at...

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  20. answer any one question : (ii) find the equation of the line which is...

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