Question Number 176213 by cortano1 last updated on 15/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{arctan}\:\mathrm{x}}{\mathrm{arcsin}\:\mathrm{x}−\mathrm{x}}\:=? \\ $$ Answered by flamable last updated on 15/Sep/22 $$ \\ $$$${By}\:{the}\:{help}\:{of}\:{Taylor}-{Young}\:{formulae}\:{at}\: \\ $$$${x}\:=\:\mathrm{0}\:{we}\:{have}\:{the}\:{following}\::…
Question Number 176199 by infinityaction last updated on 14/Sep/22 Answered by mr W last updated on 15/Sep/22 $$\left(\mathrm{1}+{x}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{C}_{{k}} ^{{n}} {x}^{{k}} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}}…
Question Number 176154 by cortano1 last updated on 14/Sep/22 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\mathrm{x}−\mathrm{x}}{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}\:=? \\ $$ Answered by adhigenz last updated on 14/Sep/22 $$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}^{\mathrm{2}} {x}−\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 176035 by cortano1 last updated on 11/Sep/22 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:−\mathrm{sin}\:\mathrm{x}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{x}} −\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }}\:= \\ $$ Answered by Ar Brandon last updated on 11/Sep/22…
Question Number 175996 by sciencestudent last updated on 10/Sep/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{a}^{{x}} −\mathrm{1}}{{x}}=? \\ $$ Answered by Ar Brandon last updated on 10/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{a}^{{x}} −\mathrm{1}}{{x}}=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 175995 by sciencestudent last updated on 10/Sep/22 $${li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{\mathrm{3}{x}} −\mathrm{1}}{{x}}=? \\ $$ Answered by Ar Brandon last updated on 10/Sep/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{3}{x}} −\mathrm{1}}{{x}}=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 175994 by sciencestudent last updated on 10/Sep/22 $${li}\underset{{x}\rightarrow\infty} {{m}}\frac{{e}^{{x}} −\mathrm{1}}{{x}}=? \\ $$ Answered by JDamian last updated on 10/Sep/22 $$\infty \\ $$ Answered…
Question Number 110440 by bemath last updated on 29/Aug/20 $$\mathrm{Given}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{f}\left(\mathrm{x}\right)+\frac{\mathrm{1}}{\mathrm{f}\left(\mathrm{x}\right)}\right)\:=\:\mathrm{2}\:,\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$ Answered by john santu last updated on 29/Aug/20 $$\:{let}\:{g}\left({x}\right)\:=\:{f}\left({x}\right)+\frac{\mathrm{1}}{{f}\left({x}\right)}\:\&\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 175967 by infinityaction last updated on 10/Sep/22 $$\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\:\left[\boldsymbol{\mathrm{tan}\Psi}+\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\mathrm{2}} }+…+\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{{n}}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\boldsymbol{{n}}} }\right]\:\:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 175880 by cortano1 last updated on 08/Sep/22 Answered by blackmamba last updated on 09/Sep/22 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{bx}^{\mathrm{2}} \left(\frac{\mathrm{sin}\:{x}}{{x}}\right)^{\mathrm{2}} +\mathrm{3}{x}\left(\frac{\mathrm{tan}\:\mathrm{3}{x}}{\mathrm{3}{x}}\right)+\mathrm{2}{x}^{\mathrm{2}} \left(\frac{\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{2}}{x}}{{x}}\right)^{\mathrm{2}} }{\:\sqrt{\mathrm{2}}\:{x}\left(\frac{\mathrm{sin}\:\frac{\mathrm{3}}{\mathrm{2}}{x}}{{x}}\right)+{x}^{\mathrm{2}{b}} \left(\frac{\mathrm{sin}\:\mathrm{3}{x}}{{x}}\right)^{\mathrm{2}{b}} }\: \\…