Question Number 131445 by rs4089 last updated on 04/Feb/21
Answered by mathmax by abdo last updated on 04/Feb/21
$$\mid\left(\mathrm{x}+\mathrm{y}\right)\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}+\mathrm{y}}\right)\mid\leqslant\mid\mathrm{x}+\mathrm{y}\mid\:\Rightarrow\mathrm{lim}_{\left(\mathrm{x},\mathrm{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} \:\:\left(\mathrm{x}+\mathrm{y}\right)\mathrm{sin}\left(\frac{\mathrm{1}}{\mathrm{x}+\mathrm{y}}\right)=\mathrm{0} \\ $$