Chapter 14.2, Problem 51E

To determine

(a)

Toshow:

That as $\left(x,y\right)\to \left(0,0\right)$ along any line $y=mx$, the limit equals 0.

To determine

(b)

Toshow:

that as $\left(x,y\right)\to \left(0,0\right)$ along any line $y=x^3$, the limit does not equals 0 hence $\underset{\left(x,y\right)\to \left(0,0\right)}{\lim }f\left(x,y\right)$ does not exist.