Question Number 105383 by bemath last updated on 28/Jul/20 $$\mathcal{G}{iven}\:\begin{cases}{\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{{f}\left({x}\right)−{a}}{{x}−\mathrm{5}}\:=\:\mathrm{8}}\\{\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −{ax}+{b}}{{f}\left({x}\right)−{a}}\:=\:\mathrm{1}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{b}+\mathrm{23}\: \\ $$ Answered by john santu last updated on 28/Jul/20…
Question Number 105331 by Ar Brandon last updated on 27/Jul/20 $$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{t}}\mathrm{ln}\left[\mathrm{1}−\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)}{\mathrm{ln}\left(\mathrm{t}\right)}\right] \\ $$ Commented by bubugne last updated on 28/Jul/20 $$ \\ $$$$=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{t}}\mathrm{ln}\left[\frac{\mathrm{ln}\left(\mathrm{t}\right)−\:\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)}{\mathrm{ln}\left(\mathrm{t}\right)}\right]…
Question Number 170766 by cortano1 last updated on 30/May/22 $$\:\:\:\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{7}}]{{x}^{\mathrm{7}} +{x}^{\mathrm{6}} −\mathrm{1}}\:+\sqrt[{\mathrm{9}}]{{x}^{\mathrm{5}} +\mathrm{1}−{x}^{\mathrm{9}} }\:=? \\ $$ Answered by aleks041103 last updated on 30/May/22 $$\sqrt[{\mathrm{7}}]{{x}^{\mathrm{7}}…
Question Number 170767 by 2407 last updated on 30/May/22 Answered by aleks041103 last updated on 30/May/22 $${L}=\underset{{x}\rightarrow\infty} {{lim}}\:\left(\frac{\mathrm{1}}{\mathrm{5}^{{x}} +\mathrm{7}^{{x}} +\mathrm{9}^{{x}} }\right)^{−\sqrt{\frac{\mathrm{1}}{{x}}}} \\ $$$$\Rightarrow{lnL}=\underset{{x}\rightarrow\infty} {{lim}}\frac{{ln}\left(\mathrm{5}^{{x}} +\mathrm{7}^{{x}}…
Question Number 105205 by Ar Brandon last updated on 26/Jul/20 Commented by Aziztisffola last updated on 26/Jul/20 $$\mathrm{ce}\:\mathrm{n}'\mathrm{est}\:\mathrm{pas}\:\mathrm{tres}\:\mathrm{lisible}. \\ $$ Commented by Ar Brandon last…
Question Number 39635 by math khazana by abdo last updated on 09/Jul/18 $${calculate}\:\:{lim}_{{x}\rightarrow\mathrm{1}} \:\frac{\mathrm{1}+{cos}\left(\pi{x}\right)}{{x}^{\mathrm{2}} −\:{sin}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 105157 by bramlex last updated on 26/Jul/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:^{\mathrm{2}} \left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)−\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}+\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{2}}\:? \\ $$ Answered by bramlex last updated on 26/Jul/20 $$\mathrm{cos}\:^{\mathrm{2}} \left(\frac{\mathrm{3}{x}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{cos}\:\mathrm{3}{x}+\mathrm{1}\right) \\ $$$$\underset{{x}\rightarrow\pi/\mathrm{6}}…
Question Number 105126 by bemath last updated on 26/Jul/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}+\mathrm{cos}\:{x}−\sqrt{\mathrm{2}}\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}−\mathrm{cos}\:{x}} \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jul/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{\mathrm{cosx}−\mathrm{sinx}−\sqrt{\mathrm{2}}\mathrm{sec}^{\mathrm{2}} \mathrm{x}}{\mathrm{cosx}+\mathrm{sinx}}=\frac{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\sqrt{\mathrm{2}}.\mathrm{2}}{\:\sqrt{\mathrm{2}}}=−\mathrm{2} \\…
Question Number 105114 by john santu last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{3}{x}\right)}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)}}{{x}^{\mathrm{2}} } \\ $$ Answered by bemath last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 105104 by bemath last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:^{\mathrm{5}} \left({x}\right)\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{2}{x}\right)\mathrm{cos}\:^{\mathrm{3}} \left(\mathrm{3}{x}\right)}{\mathrm{22}{x}^{\mathrm{2}} }? \\ $$ Answered by bramlex last updated on 26/Jul/20 $$\underset{{x}\rightarrow\mathrm{0}}…