Chapter 14.2, Problem 43E

To determine

(a)

Toshow:

$\left|x^3\right|\le \left|x\right|\left(x^2+y^2\right)$ and $\left|y^3\right|\le \left|y\right|\left(x^2+y^2\right)$

To determine

(b)

Toshow:

$\left|f\left(x,y\right)\right|\le \left|x\right|+\left|y\right|$

To determine

(c)

Toprove:

$\underset{\left(x,y\right)\to \left(0,0\right)}{\lim }f\left(x,y\right)=0$ by using squeeze theorem.