Question Number 216953 by mustaphapelumi last updated on 25/Feb/25
Commented by Ghisom last updated on 26/Feb/25
![or use l′Ho^ pital lim_(x→0) ((sin x)/x) =lim_(x→0) (((d[sin x])/dx)/((d[x])/dx)) =lim_(x→0) ((cos x)/1) =1](https://www.tinkutara.com/question/Q216977.png)
$$\mathrm{or}\:\mathrm{use}\:\mathrm{l}'\mathrm{H}\hat {\mathrm{o}pital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{{d}\left[\mathrm{sin}\:{x}\right]}{{dx}}}{\frac{{d}\left[{x}\right]}{{dx}}}\:=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}}{\mathrm{1}}\:=\mathrm{1} \\ $$