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June 1st, 2017, 03:23 AM   #1
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Integration

The functions $f(z)$ and $g(z)$ are such that the function $F= (2x+yf(z))i+(2y+xf(z))j+xyg(z)k$ can be written as a gradient of some scalar function. Pick up the possible choices for $f$ and $g$ from the following.

A) $f(z) = z^3$ and $g(z)= 3z^2 $
B) $f(z) = 0$ and $g(z)= 0 $
C) $f(z) = 1$ and $g(z) = 0$
D) $f = 1$ and $g= z$

I didn't understand the question itself. Please someone help!!
Thank you
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June 1st, 2017, 09:00 AM   #2
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Can $2x + yf(z)$, $2y + xf(z)$ and $xyg(z)$ be the partial derivatives with respect to $x$, $y$ and $z$ respectively of some (scalar) function of $x$, $y$ and $z$?
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June 1st, 2017, 05:11 PM   #3
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Option A & B can be represented as a partial derivative of $x^2+xyz^3+y^2$ and $x^2+y^2$.

Please correct me If wrong.
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