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∫(1)∂z = z

Does this even make sense? I came up with this in my differential equations class, but I'm not sure if it actually means anything.

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- Thread starter caleb5040
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- #1

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∫(1)∂z = z

Does this even make sense? I came up with this in my differential equations class, but I'm not sure if it actually means anything.

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HallsofIvy

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I think that makes sense. Thanks!

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HallsofIvy

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[tex]\frac{\partial f}{\partial x}= 1[/tex]

[tex]\frac{\partial f}{\partial y}= 1[/tex]

[tex]\frac{\partial f}{\partial z}= 1[/tex]

The last equation gives, as I said, f(x,y,z)= z+ g(x,y). Differentiating that with respect to y,

[tex]\frac{\partial f}{\partial y}= \frac{\partial g}{\partial y}= 1[/tex]

so that g(x,y)= y+ h(x). Differentiating that with respect to x,

[tex]\frac{\partial g}{\partial x}= \frac{dh}{dx}= 1[/tex]

which gives h(x)= x+ C. Putting all of those together, f(x,y,z)= z+ g(x,y)= z+ y+ h(x)a= z+ y+ x+ C.

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