Question Number 197110 by cortano12 last updated on 08/Sep/23
Answered by MathematicalUser2357 last updated on 10/Sep/23
$$\mathrm{let}\:{f}\left({x}\right)=\frac{\sqrt[{\mathrm{3}}]{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }−\mathrm{2}\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{4}}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\mathrm{Then}\:\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=\infty \\ $$$$\mathrm{and}\:\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}{f}\left({x}\right)=−\infty \\ $$