Determine Whether the Vector Field Is Conservative $\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$

question 102

Multiple Choice

Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
$\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$

• A) conservative with potential function \(f ( x , y , z ) = x ^ { 10 } y\)
• B) conservative with potential function \(f ( x , y , z ) = x y ^ { 10 }\)
• C) conservative with potential function \(f ( x , y , z ) = x ^ { 11 } y\)
• D) conservative with potential function \(f ( x , y , z ) = x y ^ { 11 }\)
• E) not conservative

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