# Recitation 7

Section 11.4 Problem 4: Find an equation of the tangent plane to the given surface at the specified point. $z=xe^{xy}; (2,0,2)$

Section 11.4 Problem 17: Given that f is a differentiable function with $f(2, 5)=6, f_x (2, 5)=1$, and $f_y(2, 5) = -1$, use a linear approximation to estimate $f(2.2, 4.9)$.

Section 11.4 Problem 20: Find the differential of the function. $u=\sqrt{x^2+3y^2}$.

Section 11.4 Problem 25: If $z=5x^2+y^2$ and $(x, y)$ changes from $(1, 2)$ to $(1.05, 2.1)$, compare the values of $\Delta z$ and $dz$.

Section 11.4 Problem 37: Prove that if $f$ is a function of two variables that is differentiable at $(a, b)$, then $f$ is continuous at $(a, b)$.

Section 11.5 Problem 18: Use the Chain Rule to find the indicated partial derivatives. $T=\frac{v}{2u+v}, u=pr\sqrt{r}, v=p\sqrt{q}r$; $\frac{\partial T}{\partial p}, \frac{\partial T}{\partial q}, \frac{\partial T}{\partial r}$ when $p=2, q=1, r=4$.

Section 11.5 Problem 27: Use $\frac{\partial z}{\partial x}=-\frac{\partial F/\partial x}{\partial F/\partial z}, \frac{\partial z}{\partial y}=-\frac{\partial F/\partial y}{\partial F/\partial z}$ to find $\partial z/\partial x$ and $\partial z/\partial y$. $e^z=xyz$.

Section 11.5 Problem 39: If $z=f(x-y)$, show that $\partial z /\partial x + \partial z/\partial y =0$.