- #1
seang
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I'm really having trouble with this, I can't even understand the example in my textbook. The example problem is:
Show that ydx + xdy + 4dz is exact and then evaluate it over some limits.
I can show that its exact, and once I find the function, I can evaluate it, so I really just need help getting the function. So the book says:
df/dx = y; df/dy = x; df/dz = 4; I understand this part, then the next step is:
f(x,y,z) = xy + g(y,z); Got this too, but now the fun begins. The next line is:
df/dy = x + dg/dy = x or dg/dy = 0; I have no idea what they're talking about here. Where is the dg/dy from? And why is 'x' what the equation is supposed to equal? The next step is:
f(x,y,z) = xy + h(z); followed by:
df/dz = 0 + dh/dz = 4 or h(z) = 4z + C; Again, I have no idea where the dh/dz if from. Also, above df/dz = 4, now it is 0? I understand that if you differentiate 4, you get 0, but what's with the discrepancy?
Any help is appreciated! I know this is long so thanks for your time
Show that ydx + xdy + 4dz is exact and then evaluate it over some limits.
I can show that its exact, and once I find the function, I can evaluate it, so I really just need help getting the function. So the book says:
df/dx = y; df/dy = x; df/dz = 4; I understand this part, then the next step is:
f(x,y,z) = xy + g(y,z); Got this too, but now the fun begins. The next line is:
df/dy = x + dg/dy = x or dg/dy = 0; I have no idea what they're talking about here. Where is the dg/dy from? And why is 'x' what the equation is supposed to equal? The next step is:
f(x,y,z) = xy + h(z); followed by:
df/dz = 0 + dh/dz = 4 or h(z) = 4z + C; Again, I have no idea where the dh/dz if from. Also, above df/dz = 4, now it is 0? I understand that if you differentiate 4, you get 0, but what's with the discrepancy?
Any help is appreciated! I know this is long so thanks for your time