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Find the equation of the normal to the c...

Find the equation of the normal to the curve `y=(logx)^2` at `x=frac[1][e]`.

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MODERN PUBLICATION-SAMPLE PAPER 2017-EXERCISE
  1. Write the interval in which the function sin^2x-x is increasing.

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  2. Verify Cauchy's mean value for the functions f(x)=sinx, g(x)=cosx in [...

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  3. Find the equation of the normal to the curve y=(logx)^2 at x=frac[1][e...

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  4. If U=ln(x^3+y^3+z^3-3xyz), show that frac[deltau][deltax]+frac[deltau...

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  5. Evaluate:underset(xto1)(lim)1/x^(1-x)

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  6. If y=x^4e^(2x),then find,dy/dx.

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  7. If y=(x+(1)/(x+(1)/(x+ . . .oo))) find (dy)/(dx), the rhs being a vali...

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  8. What is the derivative of sec^(-1)(1/(2x^2-1)),with respect to(sqrt(1...

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  9. Solve the following differential equation (x+2y^(3))dy/dx=y.

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  10. Solve the following second order equations cosec x(d^(2)y)/(dx^2)=x

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  11. Evaluate : intx^(2)tan^(-1)xdx.

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  12. int0^ax^3(a^2-x^2)^(5/2)dx

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  13. Evaluate:int0^a dx/(e^(4x)-5)

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  14. Evaluate int-1^2 {|x\|+[x]}dx

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  15. Find the feasible region of the system. 2y-xge0,6y-3xle21,xge0,yge0

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  16. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  17. Find the co-ordinates of the point where the perpendicular from the or...

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  18. Find the value of a for which the plane x+y+z-a=0 will touch the spher...

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  19. If vecp=frac[1][lambda](vecbtimesvecc),vecq=frac[1][lambda](vecctimes...

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  20. Find the equation of the plane through the point (2,1,0) and passing t...

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