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If u = x/y^2- y/x^2 , show that (del^2u)...

If `u = x/y^2- y/x^2` , show that `(del^2u)/(delxdely)=(del^2u)/(delydelx)`.

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FULL MARKS-DIFFERENTIALS AND PARTIAL DERIVATIVES -Additional Questions Solved
  1. If U = (x-y) (y-z) (z-x) then show that Ux+Uy+Uz = 0

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  2. If u=x^2+3xy+y^2 Verify (del^2u)/(delxdely)=(del^2u)/(delydelx).

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  3. If u = x/y^2- y/x^2 , show that (del^2u)/(delxdely)=(del^2u)/(delydelx...

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  4. Suppose that z=ye^(x^2) where x = 2t and y = 1 then find (dz)/(dt)

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  5. If w=x+2y+z^2and x= cos t , y = sin t, z = t Find (dw)/(dt) .

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  6. If f(x,y) = 1/(sqrt(x^2+y^2)) then show that x(delf)/(delx)+y(delf)/...

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  7. Using Euler's theorem , prove that x(delu)/(delx)+y(delu)/(dely)=1/2ta...

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  8. If u= x^y then is equal to ..........

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  9. If u= sin^(-1)((x^(4) + y^(4))/(x^(2) + y^(2))) and f= sin u then f is...

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  10. If u=1/(sqrt(x^2+y^2)) , then x(delu)/(delx)+y(delu)/(dely) is equal t...

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  11. The curve y^2(x-2)=x^2(1+x) has .......

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  12. If x= r cos theta, y = r sin theta, then (del r)/(del x)=

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  13. If u=log((x^2+y^2)/(xy)) then x(delu)/(delx)+y(delu)/(dely) is ..........

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  14. The percentage error in the 11th root of the number 28 is approximatel...

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  15. The curve a^2y^2=x^2(a^2-x^2) has .......

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  16. An asymptote to the curve y^2(a+2x)=x^2(3a-x) is ...........

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  17. In which region the curve y^2(a+x)=x^2(3a-x) does not lie ?

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  18. If u= y sin x then (del^(2)u)/(del x del y)=

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  19. If u=f(y/x), then x(del u)/(del x) + y(del u)/(del y)=

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  20. The curve 9y^2=x^2(4-x^2) is symmetrical about .......

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