Question Number 58867 by malwaan last updated on 01/May/19
$$\mathrm{1}:\:\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{sin}\left(\frac{\mathrm{1}}{{x}}\right) \\ $$$$\mathrm{2}:\:\underset{{x}\rightarrow\infty} {{lim}}\:{sin}\left({x}\right) \\ $$
Commented by tanmay last updated on 01/May/19
$$\left.\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{sin}\left(\frac{\mathrm{1}}{{x}}\right)\: \\ $$$${the}\:{limiting}\:{value}\:{lies}\:{between}\:\pm\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{t}=\frac{\mathrm{1}}{{x}}\:{when}\:{x}\rightarrow\infty\:\:{t}\rightarrow\mathrm{0} \\ $$$$\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{sin}\left(\frac{\mathrm{1}}{{t}}\right) \\ $$$${the}\:{limiting}\:{value}\:{lies}\:{between}\:\pm\mathrm{1} \\ $$$${attaching}\:{graph}\:{for}\:{clarity}. \\ $$$$ \\ $$
Commented by tanmay last updated on 01/May/19
Commented by tanmay last updated on 01/May/19
Commented by malwaan last updated on 01/May/19
$$\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\:{sin}\left(\frac{\mathrm{1}}{{x}}\right)\rightarrow+\mathrm{ve} \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{−} } {{lim}}\:{sin}\left(\frac{\mathrm{1}}{{x}}\right)\rightarrow−\mathrm{ve} \\ $$$$\therefore\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{sin}\left(\frac{\mathrm{1}}{{x}}\right)\:{does}\:{not}\:{exist} \\ $$$${Am}\:{I}\:{right}\:? \\ $$$${please}\:{check}\:.... \\ $$