Question Number 183162 by mnjuly1970 last updated on 21/Dec/22 Answered by aleks041103 last updated on 23/Dec/22 $${sin}\left({x}\right)={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+{o}\left({x}^{\mathrm{3}} \right) \\ $$$$\Rightarrow−\frac{{sin}\left({x}\right)}{{x}}=−\mathrm{1}+\frac{{x}^{\mathrm{2}} }{\mathrm{6}}+{o}\left({x}^{\mathrm{2}} \right)\rightarrow−\mathrm{1}^{+} \\ $$$$−\frac{{x}}{{sin}\left({x}\right)}\rightarrow−\mathrm{1}^{−}…
Question Number 183136 by mathlove last updated on 21/Dec/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sinx}−{x}}{{x}^{\mathrm{3}} }=? \\ $$ Answered by TheSupreme last updated on 21/Dec/22 $${sin}\left({x}\right)={x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+{o}\left({x}^{\mathrm{4}} \right) \\…
Question Number 117551 by bobhans last updated on 12/Oct/20 $$\left(\mathrm{a}\right)\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{2}\left(\mathrm{1}−\sqrt{\mathrm{x}}\right)}\:−\frac{\mathrm{1}}{\mathrm{3}\left(\mathrm{1}−\sqrt[{\mathrm{3}\:}]{\mathrm{x}}\:\right)}\right)\:=? \\ $$$$\left(\mathrm{b}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\:−\mathrm{ln}\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:\right)}{\left(\mathrm{ln}\:\left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)\right)^{\mathrm{2}} }=? \\ $$ Answered by bemath last updated on…
Question Number 117545 by Lordose last updated on 12/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left(\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \left(\sqrt{\mathrm{x}}\right)\right)^{\frac{\mathrm{1}}{\mathrm{2x}}} \\ $$ Answered by TANMAY PANACEA last updated on 12/Oct/20 $${lny}=\underset{{x}\rightarrow\mathrm{0}+} {\mathrm{lim}}\:\frac{{ln}\left(\mathrm{1}+{tan}^{\mathrm{2}}…
Question Number 51980 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{\mathrm{2}{n}+\mathrm{1}} \:\:\:\:\frac{\mathrm{1}}{\:\sqrt{{n}^{\mathrm{2}} +{k}}}\:\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 117498 by bobhans last updated on 12/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }−\mathrm{1}}\:? \\ $$ Answered by bemath last updated on 12/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }−\mathrm{1}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}−\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}}…
Question Number 182978 by TUN last updated on 18/Dec/22 Answered by dumitrel last updated on 18/Dec/22 $$ \\ $$ Commented by dumitrel last updated on…
Question Number 117422 by bemath last updated on 11/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3tan}\:\mathrm{4x}−\mathrm{4tan}\:\mathrm{3x}}{\mathrm{3sin}\:\mathrm{4x}−\mathrm{4sin}\:\mathrm{3x}}\:=? \\ $$ Answered by bobhans last updated on 11/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3tan}\:\mathrm{4x}−\mathrm{4tan}\:\mathrm{3x}}{\mathrm{3sin}\:\mathrm{4x}−\mathrm{4sin}\:\mathrm{3x}}\:=\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}\left(\mathrm{4x}+\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{4x}\right)^{\mathrm{3}}…
Question Number 117416 by Lordose last updated on 11/Oct/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } −\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}} \\ $$ Answered by Olaf last updated on 11/Oct/20 $$\forall{x}\in\mathbb{R},\:\mathrm{sin}{x}\:\leqslant\:{x}\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}}\:\geqslant\:\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 117417 by bobhans last updated on 11/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\mathrm{tanh}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\frac{\mathrm{1}}{\mathrm{cosh}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} =? \\ $$ Answered by Lordose last updated on 11/Oct/20 $$\mathrm{1} \\ $$…