Functions of Several Variables; Partial Differentiation; and Total Differentiation
Functions of Several Variables; Partial Differentiation; and Total Differentiation Exercise 1 : Table of Variables Construct a table of values for the function $f(x, y) = x^2 y + 6$ where $x = -2, -1, 0, 1$ and $y = -2, -1, 0, 1, 2$. Exercise 2 : Plane and Quadratic Surfaces What surfaces are represented by the following functions? Sketch them! $z = -x - 2y + 2$ $z = x^2 + y^2$ $z = \sqrt{1 - \frac{x^2}{4} - \frac{y^2}{9}}$ Exercise 3 : Partial Derivatives — Practice Obtain the partial derivatives of ...