Chapter 14 - Partial Derivatives - 14.2 Exercises - Page 924: 27

Discontinuous along the line $y=x$

Consider the function $f(x,y)=e^{1/x-y}$ Use maple command to plot the graph of the function as depicted below: Suppose $x-y=0$ $y=x$ Therefore, the function $f(x,y)=e^{1/x-y}$is discontinuous at all points which satisfy $y=x$ Hence, the function is discontinuous along the line $y=x$