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Question-171706




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
lim_(x→1) ((1−x^3 )/(cos (π/(x+1))))  =lim_(x→1) ((−3x^2 )/((π/((x+1)^2 ))sin (π/(x+1))))  =((−3)/(π/4))  =−((12)/π)
$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{1}−{x}^{\mathrm{3}} }{\mathrm{cos}\:\frac{\pi}{{x}+\mathrm{1}}} \\ $$$$=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{−\mathrm{3}{x}^{\mathrm{2}} }{\frac{\pi}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{sin}\:\frac{\pi}{{x}+\mathrm{1}}} \\ $$$$=\frac{−\mathrm{3}}{\frac{\pi}{\mathrm{4}}} \\ $$$$=−\frac{\mathrm{12}}{\pi} \\ $$

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