91Ó°ÊÓ

Determine whether each limit exists. If it does, find the limit and prove that it is the limit; if it does not, explain how you know. $$ \lim _{(x, y) \rightarrow(0,0)} \frac{x^{4}-y^{4}}{x^{2}+y^{2}} $$

Find all first and second partial derivatives of \(z\) with respect to \(x\) and \(y\) if \(x y+y z+x z=1 .\)

A trough is to be formed by bending up two sides of a long metal rectangle so that the cross-section of the trough is an isosceles trapezoid. If the width of the metal sheet is 2 meters, how should it be bent to maximize the volume of the trough?