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If sin (x + y) = y cos (x + y) then prov...

If sin (x + y) = y cos (x + y) then prove that
`dy/dx =-(1 + y^2)/y^2`

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2)) in the form of ...

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  2. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  3. Discuss the continuity and differentiability of function f(x)=|x|+|x-1...

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  4. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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  5. Find dy/dx for (x+y)^(cosx) = e^(x+y).

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  6. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  7. Evaluate : int (cos px + cos qx)/(sin px + sin qx) dx.

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  8. Evaluate int (4x-5)/(x^2-x-2)dx

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  9. FInd the area of the region bounded by y^2 = x and y = x.

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  10. Solve : dy/dx (x^2 - 1) + 2xy = 1.

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  11. Form the differential equation for : y = a sin^-1 x + b cos^-1 x.

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  12. Find the point of intersection of the line 2x - 4= 3y = z with plane x...

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  13. Find the equation of the plane parallel to x - 5y + z + 1 =0 and at a ...

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  14. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  15. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

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  16. Exaniming consistency and solvability, solve the following equations b...

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  17. Prove that e^x-2=0 has a solution between 0 and 1.

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  18. Show that the radius of the right cicular cylinder of greatest curved ...

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  19. Evaluate int(0)^(pi//2)logsinxdx.

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  20. Find the distance of the point (1,-2,3) from the plane x-y+z=5, measur...

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