Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. (If the vector field is not conservative, enter DNE.) F(x, y) = (yex + sin(y))i + (ex + x cos(y))j
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A vector field F is conservative if its curl is zero. The curl of a vector field F = P(x, y)i + Q(x, y)j is given by ∂Q/∂x - ∂P/∂y. Here, P(x, y) = yex + sin(y) and Q(x, y) = ex + x cos(y). So, ∂Q/∂x = ex - x sin(y) and ∂P/∂y = ex + cos(y). We see that ∂Q/∂x = Show more…
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