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[0//1 Points]
DETAILS
MY NOTES
SCALCET9 16.3.007.
Determine whether or not F is a conservative vector field. If It is, find a function
f such that F = Vf. (If the vector field is not conservative, enter DNE.)

F(x,y)=◻(x,y)=(ye^(x)+sin(y))1+(e^(x)+x cos(y))j

$4$ . $[0 / 1$ Points] $\newline$ DETAILS $\newline$ MY NOTES $\newline$ SCALCET $9$ $16$ . $3$ . $007$ . $\newline$ Determine whether or not F is a conservative vector field. If It is, find a function $f$ such that F = Vf. (If the vector field is not conservative, enter DNE.) $\newline$ $F(x, y)=\square(x, y)=\left(y e^{x}+\sin (y)\right) 1+\left(e^{x}+x \cos (y)\right) j$

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Find the magnitude of a vector

Full solution

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4

.

[0 / 1

Points]

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DETAILS

\newline

MY NOTES

\newline

SCALCET

9

16

.

3

.

007

.

\newline

Determine whether or not F is a conservative vector field. If It is, find a function

f

such that F = Vf. (If the vector field is not conservative, enter DNE.)

\newline

F(x, y)=\square(x, y)=\left(y e^{x}+\sin (y)\right) 1+\left(e^{x}+x \cos (y)\right) j

Identify components of $F(x, y)$ : Identify the components of the vector field $F(x, y)$ given by $F(x, y) = (y e^x + \sin(y))\mathbf{i} + (e^x + x \cos(y))\mathbf{j}$ .
Check for conservativity: Check if $F$ is conservative by verifying if the partial derivative of $M$ with respect to $y$ equals the partial derivative of $N$ with respect to $x$ , where $M = y e^x + \sin(y)$ and $N = e^x + x \cos(y)$ .
Calculate partial derivatives: Calculate $\partial M/\partial y = e^x + \cos(y)$ and $\partial N/\partial x = e^x - \sin(y)$ .

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