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Solve the Problem z=f(x,y)z = f ( x , y )

Question 213

Essay

Solve the problem.
-For the surface z=f(x,y)z = f ( x , y ) , show that the surface integral g(x,y,z)dσ=\iint g ( x , y , z ) d \sigma = g(x,y,f(x,y))[fx(x,y)]2+[fy(x,y)]2+1dxdy\iint \mathrm { g } ( \mathrm { x } , \mathrm { y } , \mathrm { f } ( \mathrm { x } , \mathrm { y } ) ) \sqrt { \left[ \mathrm { f } _ { \mathrm { x } } ( \mathrm { x } , \mathrm { y } ) \right] ^ { 2 } + \left[ \mathrm { f } _ { \mathrm { y } } ( \mathrm { x } , \mathrm { y } ) \right] ^ { 2 } + 1 } \mathrm { dx } d y

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