Question Number 13252 by raktim Ghosh last updated on 17/May/17
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}sin}\:\mathrm{x} \\ $$
Answered by Abbas-Nahi last updated on 17/May/17
$$={x}\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\:\frac{\mathrm{sin}\:{x}}{{x}} \\ $$$$=\mathrm{0}\:\left(\mathrm{1}\right)\:\:;{since}\left({li}\underset{×\rightarrow\mathrm{0}} {{m}}\frac{\mathrm{sin}\:{x}}{{x}}\:=\mathrm{1}\right) \\ $$$$=\mathrm{0} \\ $$
Commented by mrW1 last updated on 17/May/17
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{sin}\:{x}=\mathrm{sin}\left(\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}\right)=\mathrm{sin}\:\:\mathrm{0}=\mathrm{0} \\ $$$${just}\:{like}\:{you}\:{do}\:{with}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}=\mathrm{0} \\ $$