Chapter 13.2, Problem 34ES

(a) Show that as $\left(x,y\right)\to \left(0,0\right)$ along any straight line $y=mx,$ or along any parabola $y=k{x}^2,$ the value of $\frac{x^{3}y}{2x^6+y^2}$ approaches 0.

(b) Show that $\underset{\left(x,y,z\right)\to \left(0,0,0\right)}{\lim }\frac{xyz}{x^2+y^4+z^4}$ does not exist by letting $\left(x,y\right)\to \left(0,0,\right)$ along the curve $y=x^3.$