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A function f (x,y) is said to be harmoni...

A function `f (x,y)` is said to be harmonic if `(del^(2)f)/(del x ^(2)) + (del^(2)f)/(dely^(2)) =`

A

0

B

1

C

`-1`

D

none of the these

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The correct Answer is:
A
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PREMIERS PUBLISHERS-DIFFERENTIALS AND PARTIAL DERIVATIVES-PROBLEMS FOR PRACTICE
  1. lim ((x,y) to(1,0))(x ^(2) + y ^(2))/(x - 2y ) is :

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  2. f (x,y)=sin ^(-1) ((x)/(y)) + tan ^(-1) ((y)/(x)) is homogeneous funct...

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  3. A function f (x,y) is said to be harmonic if (del^(2)f)/(del x ^(2)) +...

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  4. If f (x,y) =e ^(2x+3y) find 3f(x) (0,0) - 2f(y) (0,0):

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  5. Find dy if y = (x-2)/( 2x +3) for x =2, dx =1.

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  6. If u =x ^(2) + y ^(2) evaluate (del^(2)f)/(del x ^(2)) + (del ^(2) f)/...

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  7. If u (x,y) = (x ^(2))/( y)- (2y ^(2))/(x) then (del^(2) u)/(del x dely...

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  8. If f (x,y) is homogeneous function of degree 5 then x (del f)/(delx) +...

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  9. Computer the values of dy if f (y) =x ^(3) +x ^(2) -2x +1 where x chan...

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  10. use differentials to find the approximate value of root 3 65.

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  11. Find the differential dy for given x and dx, y = (x ^(2) +5) ^(3),x =1...

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  12. The approximate value of 1/(10.1).

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  13. If u = x^(4) + y ^(3) + 3x ^(2) y^(2) + 3x ^(2) y find (del u)/(delx),...

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  14. If u =x ^(3) +2xy^(2) -x ^(2)y show that (del^(2)u)/(delxdely) =(del^(...

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  15. If w = u^(2)e ^(v) where u = x/y, v = y log x find (delw)/(delx)

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  16. If u =sqrt(x ^(4) +y ^(4)) show that x (delu)/(delx) + y ( del u)/(del...

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  17. If w = e ^(xy) wh4ere x = t ^(2), y = t ^(3) show that (dw)/(dt)=5t ^(...

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  18. If w=xy + z, where x=cos t, y = sin t, z=t, find (dw)/(dt).

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  19. If u =tan^(-1)((x ^(4) +y ^(4))/(x ^(2)-y ^(2))) show that x (delu)/(d...

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  20. Find (26)^((1)/3)).

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