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.

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