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Evaluate: lim(n rarr infty)[1/n+1/(n+1)+...

Evaluate: `lim_(n rarr infty)[1/n+1/(n+1)+1/(n+2)+ cdot cdot cdot +1/(3n)]`.

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MAHAVEER PUBLICATION-APPLICATION OF INTEGRALS-QUESTION BANK
  1. Find the center and radius of the circle x^2+y^2+8x+10y-8=0.

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  2. Find the equation of the parabola with vertex (0,0) and passing throug...

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  3. In what ratio does the origin divides the line segment joining the poi...

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  4. Find the direction cosines of the line whose direction ratios are 2,-4...

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  5. If g(x)=2^x, show that g(a).g(b) = g(a+b).

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  6. Find lim(x rarr2)(x^2-9x+14)/(x^2+9x-22)

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  7. Examine the continuity of f(x) at x=0 if f(x)=(sin 2x)/(2x), x ne 0

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  8. Find dy/dx:y= sqrt (1+x^2)

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  9. Find dy/dx: x=(2at)/(1+t^2), y=(a(1-t^2))/(1+t^2)

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  10. Find dy/dx if xy=sinx.

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  11. Find the maximum and minimum values of the function y=4x^3 -15x^2 +12x...

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  12. Find the unit vector in the direction of the vector vec a + vec b if v...

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  13. Integrate: int cos ecx (cos ecx +cot x) dx

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  14. Integrate: int 6x(3x^2+7)^7 dx

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  15. If (x+y, x-y)=(1,2), find x and y.

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  16. Find the value of int 0^(pi/4)(sec^2 xdx)/(1+tan^2 x)

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  17. Using the properties of the definite integral, prove that int0^(pi/2)(...

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  18. Find the area of the region bounded by the parabola y^2=4ax and the li...

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  19. Evaluate: lim(n rarr infty)[1/n+1/(n+1)+1/(n+2)+ cdot cdot cdot +1/(3n...

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  20. If y= Ae^(mx) + Be^(-mx), show that (d^2y)/dx^2-m^2y=0.

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