REVIEW PROBLEMS FOR TEST II

The University of Akron
Department of Mathematics
Calculus III
Spring 2026, Golovaty

REVIEW PROBLEMS FOR TEST II - Part I

Problem 1. Determine whether the following statements are true or false. Justify your answers.

If and then the function is differentiable at the point , that is the surface can be approximated by a tangent plane near the point .
If $f(x,y)=e^x\,,$ then $f'(x,y)=e^x\,.$
The function $f(x,y)=e^{-x}\sin{y}$ satisfies the differential equation $f_x=f_{yy}$ .

Problem 2. Find the points on the ellipsoid where the tangent plane is parallel to the plane . For one of these points find the equation of the tangent plane.

Problem 3. Find the linearization of the function $f(x\,,y)=\frac{x}{y^2}$ near the point $(4\,,-2)$ . Explain why is differentiable near $(4\,,-2)$ and use the linear approximation to approximate .