Question Number 219731 by Nescio last updated on 01/May/25
Answered by breniam last updated on 03/May/25
$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }×\frac{{x}}{\mathrm{log}\left(\mathrm{1}+\mathrm{2}{x}\right)}×\mathrm{tan}\left({x}\right)={L} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} }=\mathrm{1} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}}{\mathrm{log}\left(\mathrm{2}{x}+\mathrm{1}\right)}\overset{{H}} {=}\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\frac{\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}tan}\left({x}\right)=\mathrm{0} \\ $$$${L}=\mathrm{0} \\ $$