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Parts (a)-(d) are distinct from each other. (a) Let $F(x,y,z)=x_{2}y+xe_{yz}$. Find the equation of the tangent plane to the level surface $F(x,y,z)=0$ at the point $P(?1,1,0)$, and express it in th form $ax+by+cz+d=0$. (b) Find $?s?z?$ where $z=x_{3}+3xy_{2}+y_{2},x=rs?$, and $y=x1?$. (c) Find the directional derivative of the function $f(x,y)=x_{3}+3xy_{2}+y_{2}$ at the point $P(?1,1,?3)$ in the direction of the vector $41+3j$. (d) Use the method of Lagrange multipliers to find the maximum and minimum values of the function $f(x,y)=3x+y$ subject to the constraint $x_{2}+y_{2}=10$.

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