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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 7-EXERCISE
  1. Prove the following : [[sinalpha,cosalpha,cos(alpha+delta)],[sinbeta,c...

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  2. Test differentiability of the following function at the indicated poin...

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

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  5. If tangents are drawn from the origin to the curve y = sin x then sho...

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  6. Test the function y = (x - 5)^5( x + 2)^2 for extreme values.

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  7. Evaluate : int ((sinxcosx)/(sin2x) - 2sinx+3)dx .

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  8. int0^(pi/2)(cosxdx)/((sinx+1)(sinx+2))

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  9. Solve : (x + 2y^3)dy/dx = y.

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  10. Find the general solution of dy/(du) = u+1/sqrtu + 6u + 5.

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  11. Prove the following by vector method. The diagonals of a rhombus are a...

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  12. Find the equation of the plane passing through the line of intersectio...

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  13. Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...

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  14. Obtain the equation of the line through the point (1, 2, 3) and parall...

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  15. Find the inverse of the following matrices using elementary transforma...

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  16. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  17. Evaluate : int ln(1+x)/(1+x) dx

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  18. Solve: xdy/dx+y=y^2ln x

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  19. Find the area of the région on closed between y = 4x-1 and y^2=2x

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  20. Prove that lveca+vecblless than or equallvecal+lvecbl .

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