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if x=e^(t)sin t and y=e^(t)cos t, then p...

if `x=e^(t)sin t` and `y=e^(t)cos t`, then prove that `(x+y)^(2)(d^(2)y)/dx^(2)=2(xdy/dx-y)`.

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
  1. Find the inverse of the following matrix [{:(0,0,2),(0,2,0),(2,0,0):}]

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  2. Examine the continuity of the following functions at indicated points....

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  3. if x=e^(t)sin t and y=e^(t)cos t, then prove that (x+y)^(2)(d^(2)y)/dx...

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  4. Differentiate. x^(sin x)+(tan x)^x

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  5. Find the equation of the normal at a point on the curve x^(2) = 4y, wh...

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  6. etermine the sub-interval of (-(pi)/(2),(pi)/(2)), in which f(x)=tan x...

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  7. Integrate the following int(x+3)/(5-x^2-4x)

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  8. int0^2[x^2]dx

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  9. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  10. Solve the following differential equations (dy)/(dx)+(y)/(x)=x^(2), ...

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  11. Show that the vector area of the triangle whosse vertices have positio...

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  12. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  13. Find the co-ordinates of the point where the line joining (3,4,-5) and...

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  14. Passing throughthe point (2,-3,1) and (-1,1-7) and perpendicular to th...

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  15. Find the direction cosines of the line which is perpendicular to the l...

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  16. Prove that f:X rarr Y is surjective iff for all A sube X,(f(A))' sube ...

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  17. Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...

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  18. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  19. Find the points on the curve y = x^2+1 which are nearest to the point ...

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  20. Evaluate int0^ pi x/(1+ sin x) dx

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