- For the function $\vec r(x,y)=(x,y,4-x^2-y^2)$, compute the partial derivatives $\frac{\partial\vec r}{\partial x}$ and $\vec r_y$. Then state the derivative $D\vec r$ and the differential $d\vec r$.
- Draw the function in the previous problem. Then state two vectors tangent to the surface at $(x,y)=(1,-2)$.
- Give equations of two tangent lines to the surface at $(x,y)=(1,-2)$.
- Give an equation of the tangent plane to the surface at $(x,y)=(1,-2)$.
- Repeat the previous 4 parts with another function.
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