Question Number 171706 by Haisokheng last updated on 20/Jun/22
Answered by cortano1 last updated on 20/Jun/22
Answered by thfchristopher last updated on 20/Jun/22
$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{1}−{x}^{\mathrm{3}} }{\mathrm{cos}\:\frac{\pi}{{x}+\mathrm{1}}} \\ $$$$=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{−\mathrm{3}{x}^{\mathrm{2}} }{\frac{\pi}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{sin}\:\frac{\pi}{{x}+\mathrm{1}}} \\ $$$$=\frac{−\mathrm{3}}{\frac{\pi}{\mathrm{4}}} \\ $$$$=−\frac{\mathrm{12}}{\pi} \\ $$