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Calculus
Level
pending
f (x, y) = 3x^{2}y i - 2xy^{3} j. What is the div f (x, y) and f rot (x, y)?
div f(x, y) = 1 - y and rot f(x, y) = -2y^{3}
div f(x, y) = 6xy - 6xy^{2} and rot f(x, y) = (-2y^{3} - 3y^{2}) k.
div f(x,y ) = 3xy and rot f(X, y) = (-6y - 2) k
div f(x, y) = 2xy^{3} and rot f(x, y) = (-3y^{3} - y) k
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1 solution
F(x, y, z) = M(x, y, z) i + N(x, y, z) j + R(x, y, z) k
Then:
M(x, y) = 3x^2y
N(x, y) = 2xy^3
Partially deriving the terms, we have:
M/y= 3x^2
M/x= 6xy
N/x= -2y^3
N/y= 6xy^2
Therefore:
div f(x,y)= 6xy - 6xy^2 = 6xy(1- y)
rot f(x, y)= (-2y^3 - 3y^2) k