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Find a Function Of f(x,y)f ( x , y ) Such That

Question 160

Multiple Choice

Find a function of f(x,y) f ( x , y ) such that ∇f=2xyi+x2j\nabla f = 2 x y \mathbf { i } + x ^ { 2 } \mathbf { j } .


A) x3yx ^ { 3 } y
B) x3y2x ^ { 3 } y ^ { 2 }
C) x3/yx ^ { 3 } / y
D) x3/y2x ^ { 3 } / y ^ { 2 }
E) x2yx ^ { 2 } y
F) 2x2y2 x ^ { 2 } y
G) 2xy+x22 x y + x ^ { 2 }
H) 2xy+2x22 x y + 2 x ^ { 2 }

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