Question Number 169803 by cortano1 last updated on 09/May/22 Answered by greougoury555 last updated on 09/May/22 $$\:{x}−\mathrm{1}=\:{y}\: \\ $$$$\:\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({y}+\mathrm{1}\right)−\left(\frac{\left({n}+\mathrm{1}\right)\left({y}+\mathrm{1}\right)^{{n}} −\mathrm{1}}{{n}}\right)^{\frac{\mathrm{1}}{{n}+\mathrm{1}}} }{{y}^{\mathrm{2}\:} }\: \\ $$$$=\:\underset{{y}\rightarrow\mathrm{0}}…
Question Number 104218 by bemath last updated on 20/Jul/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left[\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}\right)+\underset{{n}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\left[\frac{\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right)}{\left(\mathrm{1}−{x}^{\mathrm{2}^{{n}} } \right)}\right]^{\mathrm{2}^{−{n}} } }{\mathrm{ln}\:\left(\frac{\mathrm{1}}{\mathrm{1}−{x}}\right)}\right] \\ $$$$ \\ $$ Commented by…
Question Number 104217 by bemath last updated on 20/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}\:\left({x}+\mathrm{3}\right)^{\mathrm{2}} −\mathrm{tan}\:\left(\mathrm{9}\right)}{{x}}\:=\:? \\ $$ Answered by bemath last updated on 20/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}\left({x}+\mathrm{3}\right)^{\mathrm{1}} \mathrm{sec}\:^{\mathrm{2}} \left({x}+\mathrm{3}\right)^{\mathrm{2}}…
Question Number 104215 by bemath last updated on 20/Jul/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{9}^{\mathrm{3}^{\mathrm{2ln}\:{x}} } −\mathrm{9}^{\mathrm{2}^{\mathrm{ln}\:{x}} } }{\mathrm{ln}\:{x}}\:=? \\ $$ Answered by john santu last updated on 20/Jul/20…
Question Number 169711 by mnjuly1970 last updated on 06/May/22 $$ \\ $$$$\:\:\:\:{prove}\:{that}: \\ $$$$\:\: \\ $$$$\:\:{lim}_{\:{x}\:\rightarrow\:\mathrm{0}} \left(\:\frac{\mathrm{1}}{{x}^{\:\mathrm{2}} }\:\:−\:\frac{{e}^{\:{x}} }{\left({e}^{\:{x}} −\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:\frac{\mathrm{1}}{\mathrm{12}} \\ $$$$\:\:\:\:\:\: \\ $$…
Question Number 104159 by Ar Brandon last updated on 19/Jul/20 $$\mathrm{How}\:\mathrm{may}\:\mathrm{we}\:\mathrm{plot}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\sqrt{\frac{\mathrm{x}\left(\mathrm{x}+\mathrm{2}\right)}{\mathrm{x}+\mathrm{1}}}\:,\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{a}\:\mathrm{variation}\:\mathrm{table}\:? \\ $$ Commented by Ar Brandon last updated on 19/Jul/20…
Question Number 169635 by cortano1 last updated on 05/May/22 $$\:\:\:\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{7}}+\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }−\mathrm{8}}{\:\sqrt{−\mathrm{3}{x}}−\mathrm{6}+\sqrt{\mathrm{18}+\mathrm{3}{x}}}\:=? \\ $$ Commented by cortano1 last updated on 05/May/22 $$\:{by}\:{L}'{Hopital} \\ $$$$\:\underset{{x}\rightarrow−\mathrm{3}}…
Question Number 169565 by mathlove last updated on 03/May/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{a}^{{sinx}} −{c}^{{sinx}} }{{m}^{{sinx}} −{n}^{{sinx}} }=? \\ $$$$\forall\left\{{a},{c},{m},{n}\right\}\in\left[\mathrm{0},\infty\right] \\ $$ Commented by infinityaction last updated on…
Question Number 169527 by Giantyusuf last updated on 01/May/22 $$\boldsymbol{{evaluate}}\:\boldsymbol{{the}}\:\boldsymbol{{limit}}\left(\boldsymbol{{if}}\:\boldsymbol{{it}}\:\boldsymbol{{exists}}\right) \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{n}}\rightarrow\infty} \left[\frac{\sqrt{\boldsymbol{{n}}^{\mathrm{4}} −\mathrm{2}\boldsymbol{{n}}^{\mathrm{3}} }−\boldsymbol{{n}}^{\mathrm{2}} }{\boldsymbol{{n}}+\mathrm{2}}\right]^{\mathrm{3}} \\ $$ Commented by infinityaction last updated on 02/May/22…
Question Number 103979 by Study last updated on 18/Jul/20 $$\:\:{show}\:{right}\:{and}\:{left}\:{sid}\:\:\:\:{limitation}\:\:\:\: \\ $$$${of}\:\:\:{li}\underset{{x}\rightarrow\mathrm{0}} {{m}}\frac{{ln}\left({b}−{x}\right)}{{ax}} \\ $$$$ \\ $$ Commented by Study last updated on 18/Jul/20 $${help}\:{me}…