Question

# Use limit laws and continuity properties to evaluate the limit. \lim_{(x,y) \rightarrow (4,-2)}x\sqrt[3]{y^{3}+2x}

Composite functions
Use limit laws and continuity properties to evaluate the limit.
$$\displaystyle\lim_{{{\left({x},{y}\right)}\rightarrow{\left({4},-{2}\right)}}}{x}\sqrt{{{3}}}{\left\lbrace{y}^{{{3}}}+{2}{x}\right\rbrace}$$

$$\displaystyle\lim_{{{\left({x},{y}\right)}\rightarrow{\left({4},-{2}\right)}}},{x}\sqrt{{{3}}}{\left\lbrace{y}^{{{3}}}+{2}{x}\right\rbrace}$$
$$\displaystyle={\left(-{2}\right)}\cdot{{\lbrace}}\sqrt{{{3}}}{\left\lbrace{\left(-{2}\right)}^{{{3}}}+{2}\dot{{\lbrace}}{4}\right\rbrace}$$
$$=0$$