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If W = x ^(2) + y ^(2) + z^(2), x,y,z in...

If `W = x ^(2) + y ^(2) + z^(2), x,y,z in R` find the differential dW.

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The correct Answer is:
`=2 (xdx + ydy+zdz)`
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PREMIERS PUBLISHERS-DIFFERENTIALS AND PARTIAL DERIVATIVES-PROBLEMS FOR PRACTICE
  1. If W = x ^(2) + y ^(2) + z^(2), x,y,z in R find the differential dW.

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  2. The percentage error of the seventh root of 700 is approximate how man...

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  3. If u = log ((x ^(2) y + y ^(2) x)/(xy)) then x (del u)/( del x) + y (...

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  4. If z =e^((x +y)/(x -y)) then x (del xz)/(del x) + y (del z)/(dely)=

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  5. If w(x,y) =x^(y), x gt 0, then (del w)/(del x) is equal to

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

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  7. If u = (1)/(root 3 (x^(3) + y ^(2))) then x (del u)/(del x) + (del u )...

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  8. If f (x,y) =e ^(xy) then (del^(2)f)/(delx dely) at (1,1) is:

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  9. A cube of side is without the top. If the edge length varies from x (0...

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

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  11. If x = r cos theta, u = r sin theta then (del theta)/(del x) is:

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  12. If f (x,y) =x ^(2) + xy+y ^(2),x =t ,y=t ^(2) then (df )/(dt)=

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  13. If f (x) =(1)/(x +1) then its differentiate is given by :

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  14. If u (x,y) =x ^(2) + 2xy-y ^(2) then (del u)/(del x) + (delu)/(del y) ...

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  15. Linear approximation of f (x) = 2x^(2) + 3x at x =1 is:

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  16. The approximate value of sqrt (9.2) is:

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  17. If the absolute error while calculating the absolute error in volume o...

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  18. lim ((x,y) to(1,0))(x ^(2) + y ^(2))/(x - 2y ) is :

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

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

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

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