Question Number 28095 by tawa tawa last updated on 20/Jan/18 $$\underset{{x}\rightarrow\mathrm{0}^{−} } {\mathrm{lim}}\:\:\left(\mathrm{1}\:+\:\mathrm{tanx}\right)^{−\mathrm{cotx}} \\ $$ Commented by abdo imad last updated on 20/Jan/18 $$=\:{lim}_{{x}\rightarrow\mathrm{0}^{−} }…
Question Number 28088 by tawa tawa last updated on 20/Jan/18 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\:\left(\mathrm{sinx}\right)^{\left(\mathrm{tanx}\right)} \\ $$ Commented by çhëý böý last updated on 20/Jan/18 $$\underset{{x}\rightarrow\mathrm{0}^{+} }…
Question Number 28084 by tawa tawa last updated on 20/Jan/18 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\left(\mathrm{x}\:−\:\mathrm{log}_{\mathrm{e}} \mathrm{x}\right) \\ $$ Commented by çhëý böý last updated on 20/Jan/18 $$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\:\:\left({x}−{lnx}\right)…
Question Number 159142 by tounghoungko last updated on 13/Nov/21 $$\:\underset{{x}\rightarrow−\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\frac{\pi}{\:\sqrt{\mathrm{8}}}\:−\sqrt{\mathrm{2}}\:{x}.\:\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}}\:=? \\ $$ Commented by cortano last updated on 14/Nov/21 $$\:\underset{{x}\rightarrow−\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{\frac{\pi\:\mathrm{cos}\:{x}−\mathrm{4}{x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{8}}}}{\:\sqrt{\mathrm{2}}\:\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\mathrm{cos}\:{x}} \\ $$$$=\:\frac{\mathrm{1}}{\:\mathrm{2}\sqrt{\mathrm{2}}}\:\underset{{x}\rightarrow−\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\pi\mathrm{cos}\:{x}−\mathrm{4}{x}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)}…
Question Number 159130 by metamorfose last updated on 13/Nov/21 $${f}\:\in\:\mathcal{C}^{\mathrm{0}} \left(\mathbb{R},\mathbb{R}\right)\:,\:\frac{{f}\left({x}\right)}{{x}}\underset{{x}\rightarrow+\infty} {\rightarrow}\mathrm{0} \\ $$$${Does}\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:{f}\left({x}+\mathrm{1}\right)\:−\:{f}\left({x}\right)\:{exist}? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 27912 by abdo imad last updated on 16/Jan/18 $${find}\:{the}\:{sum}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\mathrm{1}}{{n}}\left(\:\:\frac{\sqrt{\mathrm{2}}}{\mathrm{1}+{i}}\right)^{{n}} . \\ $$ Commented by abdo imad last updated on 23/Jan/18 $${for}\:{z}\in\:{iR}\:\:{and}\:\:\mid{z}\mid\leqslant\:\mathrm{1}\:{we}\:{have}\:\:\sum_{{n}=\mathrm{1}}…
Question Number 158894 by mathlove last updated on 10/Nov/21 Commented by cortano last updated on 10/Nov/21 $$\:\underset{{x}\rightarrow{y}} {\mathrm{lim}}\:\frac{\left(\sqrt[{\mathrm{3}}]{{x}}\right)^{\mathrm{2}} −\left(\sqrt[{\mathrm{3}}]{{y}}\right)^{\mathrm{2}} }{{x}−{y}} \\ $$$$=\:\underset{{x}\rightarrow{y}} {\mathrm{lim}}\:\frac{\left(\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{y}}\right)\left(\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{y}}\right)}{\left(\sqrt[{\mathrm{3}}]{{x}}−\sqrt[{\mathrm{3}}]{{y}}\right)\left(\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} }+\sqrt[{\mathrm{3}}]{{xy}}+\sqrt[{\mathrm{3}}]{{y}}\right)} \\…
Question Number 27792 by abdo imad last updated on 14/Jan/18 $${find}\:{lim}_{{x}−>\mathrm{1}} \int_{{x}} ^{{x}^{\mathrm{2}} } \:\:\frac{{dt}}{{ln}\left({t}\right)}\:\:. \\ $$ Commented by abdo imad last updated on 15/Jan/18…
Question Number 27789 by abdo imad last updated on 14/Jan/18 $${find}\:\:{lim}_{{x}−>\mathrm{0}} \left(\mathrm{1}+{sinx}\right)^{\frac{\mathrm{1}}{{x}}} \:\:. \\ $$ Commented by abdo imad last updated on 15/Jan/18 $${we}\:{have}\:\left(\mathrm{1}+{sinx}\right)^{\frac{\mathrm{1}}{{x}}} \:=\:{e}^{\frac{\mathrm{1}}{{x}}{ln}\left(\mathrm{1}+{sinx}\right)}…
Question Number 27786 by abdo imad last updated on 14/Jan/18 $${find}\:{lim}_{{x}−>\mathrm{0}} \:\left(\frac{{tanx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} . \\ $$ Commented by abdo imad last updated on 17/Jan/18 $${we}\:{have}\:\:\left(\frac{{tanx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}}…