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If y^2cot x = x^2 coty then find (dy)/(d...

If `y^2cot x = x^2 `coty then find `(dy)/(dx)`

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SHARAM PUBLICATION-MODEL QUESTION PAPER -15-EXERCISE
  1. For what value of lambda,is the function f(x)={(lambdax^2-2x,if xle0),...

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  2. If cos y = x cos(a+y) then prove that dy/dx = (cos^2(a+y))/sin a

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  3. If y^2cot x = x^2 coty then find (dy)/(dx)

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

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  5. Find two positive numbers whose product is 256 and whose sum is least.

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  6. Integrate:inta/(b+ce^x)dx

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  7. Integrate:int sec(sqrtx)/(sqrtx)dx

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  8. Prove that int0^(pi/2)(sin^nx)/(sin^nx+cos^nx)dx=pi/4

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  9. Find the area bounded by y=sinx,y=0,x=pi/2

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  10. Solve : (x+y)dy +(x-y)dx = 0.

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  11. If hati +hatj+hatk and 2hati -alphahatj+3hatk are orthogonal to each o...

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  12. If the magnitude of the difference of two unit vectors is sqrt3 then f...

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  13. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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  14. If veca=2vecb and vecc=-3vecb, then what is the angle between veca and...

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  15. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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  16. Find the value of k for which f(x)={{:((sqrt(1+kx)-sqrt(1-kx))/(x)", ...

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  17. Find the derivative of ((x-1)/(x^2+5))^-4 cos^-1((1-x^2)/(1+x^2))

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  18. Use the function f(x) = x^(1/x),x gt 0 to show that e^pi )grt pi^e.

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  19. Find the area enclosed by y=4x-1 and y^(2)=2x.

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  20. If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...

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