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Unformatted text preview: a in the set A ⊂ R n . State the Chain Rule for D ( F ◦ G )( a ). (b) (7pts) Let F ( x,y,z ) = ( x + y + z,x 3e yz ) and G ( s,t,u ) = ( st,tu,su ). Find D ( F ◦ G ) at the point (1 , 1 , 0) using the Chain Rule. 6. Let F ( x,y,z ) = xy + z + 3 xz 5 . (a) (2pts) What theorem is used to determine if the equation F ( x,y,z ) = c is solvable for z as a diﬀerentiable function of ( x,y ) near a point? (b) (3pts) Show that if F ( x,y,z ) = 4, that this equation is solvable for z as a diﬀerentiable function of ( x,y ) near the point (1 , , 1). (c) (2pts) Compute ∂z ∂x at (1 , 0). (d) (2pts) Are there any points of the surface F ( x,y,z ) = 4 where you can not solve for z as a diﬀerentiable function of ( x,y )? Clearly explain your answer....
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 Summer '08
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 Math, Calculus, Linear Algebra, Derivative, Angles, Vectors

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