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Let w(x, y, z)=(1)/(sqrt(x^(2)+y^(2)+z^(...

Let `w(x, y, z)=(1)/(sqrt(x^(2)+y^(2)+z^(2)))(x, y, z) != (0, 0, 0)`. Show that `(del^(2)w)/(delx^(2))+(del^(2)w)/(dely^(2))+(del^(2)w)/(delz^(2))=0`

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The correct Answer is:
`(del ^(2)w)/(del y ^(2)) + (del ^(2) w)/(del z ^(2))=0.`
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PREMIERS PUBLISHERS-DIFFERENTIALS AND PARTIAL DERIVATIVES-EXERCISE 8.4
  1. Find the partial derivatives of the functions at the indicated point ...

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  2. Find the partial derivatives of the functions at the indicated point ...

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  3. Find the partial derivatives of the functions at the indicated point ...

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  4. Find the partial derivatives of the functions at the indicated point ...

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  5. For each of the functions find the f (x), f (y), and show that f (xy) ...

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  6. For each of the functions find the f (x), f (y), and show that f (xy) ...

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  7. For each of the functions find the f (x), f (y), and show that f (xy) ...

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  8. If U(x,y,z) =(x^(2) + y^(2))/(xy) + 3z^(2)y, find (del U)/(dx) + (del ...

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  9. If U(x,y,z) = log(x^(3) + y^(3) +z^(3)) find (del U)/(dx) + (del U)/(d...

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  10. For each of the function find the g (xy), g (yy) and g (yx ), g (x,y...

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  11. For each of the function find the g (xy), g (yy) and g (yx ), g (x,y...

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  12. For each of the function find the g (xy), g (yy) and g (yx ), g (x,y...

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  13. Let w(x, y, z)=(1)/(sqrt(x^(2)+y^(2)+z^(2)))(x, y, z) != (0, 0, 0). Sh...

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  14. If V(x,y) = e^(x) (x cos y - y siny), then prove that (del^(2)V)/(del ...

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  15. If w(x,y) = xy + sin(xy), then prove that (del^(2) w)/(del y del x) =...

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  16. If v(x,y,z) = x^(3) + y^(3) + z^(3) + 3xyz, show that (del^(2)v)/(del ...

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  17. A firm produces two types of calculators each week, x number of type A...

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  18. A firm produces two types of calculators each week, x number of type A...

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