(Solved): Parts (a)-(d) are distinct from each other. (a) Let F(x,y,z)=x2y+xeyz. Find the equation of the tan ...

Parts (a)-(d) are distinct from each other. (a) Let $F(x,y,z)=x^{2}y+x{e}^{yz}$. 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 $\frac{?z}{?s}$ where $z=x^3+3x{y}^2+y^2,x=\sqrt{rs}$, and $y=\frac{1}{x}$. (c) Find the directional derivative of the function $f(x,y)=x^3+3x{y}^2+y^2$ 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 $x^2+y^2=10$.