Question Number 197514 by cortano12 last updated on 20/Sep/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}\:\mathrm{x}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{\mathrm{x}}\right)=? \\ $$ Answered by MM42 last updated on 20/Sep/23 $$\frac{\mathrm{1}}{{x}}={t}\Rightarrow{lim}_{{t}\rightarrow\mathrm{0}} \:{sin}\frac{\mathrm{1}}{{t}}×{sin}^{−\mathrm{1}} {t}\:=\mathrm{0} \\…
Question Number 197483 by cortano12 last updated on 19/Sep/23 $$\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\:\sqrt{\mathrm{1}−\mathrm{x}}}\:=? \\ $$ Answered by Frix last updated on 19/Sep/23 $$=\frac{−\frac{\pi}{\mathrm{2}}}{\:\sqrt{\mathrm{1}+\infty}}=\mathrm{0} \\ $$ Terms…
Question Number 197482 by cortano12 last updated on 19/Sep/23 $$\:\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{3}}\:+\mathrm{2}}{\mathrm{2x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1}}\:\right)=?\: \\ $$ Answered by Frix last updated on 19/Sep/23 $${f}\left({x}\right)=\frac{\sqrt{\mathrm{3}}{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}^{\mathrm{2}}…
Question Number 197479 by pticantor last updated on 19/Sep/23 $$\boldsymbol{{find}}: \\ $$$$ \\ $$$$\:\:\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{{m}}}\:\boldsymbol{{U}}_{\boldsymbol{{n}}} \:=\sqrt[{\mathrm{3}}]{\boldsymbol{{n}}^{\mathrm{3}} +\mathrm{2}\boldsymbol{{n}}^{\mathrm{2}} }−\sqrt[{\mathrm{3}}]{\boldsymbol{{n}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{n}}^{\mathrm{2}} }\: \\ $$ Commented by Frix…
Question Number 197469 by dragan91 last updated on 18/Sep/23 $$ \\ $$$${solve}\:{limits}\:{for}\:{functions} \\ $$$${f}\left({x}\right)={cos}\left({sgn}\left(\mathrm{1}/{x}\right)\right) \\ $$$${f}\left({x}\right)={sgn}\left({cos}\left(\mathrm{1}/{x}\right)\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Terms…
Question Number 197407 by mathlove last updated on 16/Sep/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}+\mathrm{1}}=? \\ $$ Answered by Rasheed.Sindhi last updated on 16/Sep/23 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}{{x}+\mathrm{1}}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{x}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 197301 by uchihayahia last updated on 13/Sep/23 $$ \\ $$$$\:{how}\:{do}\:{i}\:{calculate}\:{this} \\ $$$$\:\underset{{x}\rightarrow-\infty} {\mathrm{lim}}\:\frac{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2}}{{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{1}} \\ $$$$\:{multiplying}\:{both}\:{numerator} \\ $$$$\:{and}\:{denumerator}\:{by}\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} } \\…
Question Number 197281 by cortano12 last updated on 12/Sep/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{x}+\mathrm{2x}^{\mathrm{5}} }{\mathrm{3x}^{\mathrm{3}} }\:=? \\ $$ Answered by MM42 last updated on 12/Sep/23 $${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{−\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{5}}…
Question Number 197282 by cortano12 last updated on 12/Sep/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sin}\:\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} \:\right)}\:=? \\ $$ Answered by MM42 last updated on 12/Sep/23…
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…