Question Number 115195 by bemath last updated on 24/Sep/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{8}}} {\mathrm{lim}}\:\frac{\mathrm{cot}\:\mathrm{4}{x}−\mathrm{cos}\:\mathrm{4}{x}}{\left(\pi−\mathrm{8}{x}\right)^{\mathrm{3}} }\:?\: \\ $$ Answered by bobhans last updated on 24/Sep/20 $${let}\:{x}\:=\:\frac{\pi}{\mathrm{8}}+{p}\:;\:{p}\rightarrow\mathrm{0} \\ $$$$\underset{{p}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cot}\:\left(\mathrm{4}{p}+\frac{\pi}{\mathrm{2}}\right)−\mathrm{cos}\:\left(\mathrm{4}{p}+\frac{\pi}{\mathrm{2}}\right)}{\left(−\mathrm{8}{p}\right)^{\mathrm{3}}…
Question Number 115174 by bemath last updated on 24/Sep/20 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)\right)}{\:\sqrt{{x}−\mathrm{1}}}\:=\:? \\ $$ Answered by bobhans last updated on 24/Sep/20 $$\:{let}\:\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{1}}{{x}}\right)\:=\:\psi\:\Rightarrow\:\frac{\mathrm{1}}{{x}}\:=\:\mathrm{cos}\:\psi\: \\ $$$$\:{and}\:\mathrm{tan}\:\psi\:=\:\sqrt{{x}^{\mathrm{2}}…
Question Number 115167 by bemath last updated on 28/Sep/20 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:\:\left(\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\right)}{\mathrm{3}\sqrt{{x}}}\:=\:? \\ $$ Answered by bobhans last updated on 28/Sep/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:\:\left(\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{1}−{x}\right)\right)}{\mathrm{3}\sqrt{{x}}}\:=? \\…
Question Number 115162 by john santu last updated on 24/Sep/20 $$\:\left(\mathrm{1}\right)\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\mathrm{arc}\:\mathrm{sin}\:\left(\frac{\mathrm{1}−\sqrt{{x}}}{\mathrm{1}−{x}}\right)\:=? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{e}^{{x}^{\mathrm{3}} +\sqrt{\mathrm{cos}\:\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)}} \:=? \\ $$$$\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{csc}\:{x}\:.\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)\:=? \\ $$ Answered by…
Question Number 115122 by bobhans last updated on 23/Sep/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\left({x}^{\mathrm{2}} +\mathrm{2}{x}\right)\left({x}^{\mathrm{2}} +\mathrm{1}\right)}\:−\sqrt{\left({x}^{\mathrm{2}} +\mathrm{2}{x}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}\:? \\ $$ Commented by malwan last updated on 23/Sep/20 $${can}\:{we}\:{solve}\:{it}\:{with}\:{lhopital}??…
Question Number 115103 by bobhans last updated on 23/Sep/20 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\left({x}−{a}\right)\left({x}+\mathrm{2}\right)}\:−\sqrt{{x}\left({x}+\mathrm{1}\right)}\:=\:\mathrm{2} \\ $$$${then}\:{a}\:=\:? \\ $$ Commented by Dwaipayan Shikari last updated on 23/Sep/20 $$\underset{{x}\rightarrow\infty} {{l}\mathrm{im}}\frac{\left({x}−{a}\right)\left({x}+\mathrm{2}\right)−{x}^{\mathrm{2}}…
Question Number 115027 by bemath last updated on 23/Sep/20 $$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{17}\:\sqrt[{\mathrm{3}\:}]{\mathrm{ax}+\mathrm{3}}\:+\mathrm{b}}{\mathrm{x}−\mathrm{3}}\:=\:\frac{\mathrm{136}}{\mathrm{27}} \\ $$$$\mathrm{then}\:\mathrm{8a}+\mathrm{b}\:=\:? \\ $$ Answered by bobhans last updated on 23/Sep/20 $${limit}\:{form}\:\frac{\mathrm{0}}{\mathrm{0}}.\:{numerator}\:{must}\:{be}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{17}\:\sqrt[{\mathrm{3}\:}]{\mathrm{3}{a}+\mathrm{3}}\:+{b}\:=\mathrm{0};\:\:{b}\:\Rightarrow−\mathrm{17}\:\sqrt[{\mathrm{3}\:}]{\mathrm{3}{a}+\mathrm{3}}…
Question Number 114981 by bobhans last updated on 22/Sep/20 $${Without}\:{L}'{Hopital} \\ $$$$\:\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{{x}\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{5}} −\mathrm{32}}{{x}−\mathrm{1}}\:=? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{2}{x}+\sqrt{\mathrm{2}{x}+\sqrt{\mathrm{2}{x}+\sqrt{\mathrm{2}{x}+\sqrt{…}}}}}\:−\sqrt{\mathrm{2}{x}}\:=\:? \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 180485 by moh777 last updated on 12/Nov/22 $${Determine}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}\:, \\ $$$$\:{that}\:{make}\:{the}\:{function}\:{f}\left({x}\right)\:{continuity} \\ $$$${f}\left({x}\right)\:=\:\begin{cases}{{x}\:+\:\mathrm{3}\:\:\:\:\:,{x}\:\lneqq\:\mathrm{4}}\\{\mathrm{2}{ax}\:+\:{b}\:\:\:\:,{x}\:=\:\mathrm{4}}\\{{x}^{\mathrm{2}} −\mathrm{3}\:\:\:,\:{x}\:\gneqq\:\mathrm{4}}\end{cases} \\ $$ Commented by Frix last updated on 12/Nov/22 $$\mathrm{this}\:\mathrm{is}\:\mathrm{not}\:\mathrm{possible},\:\mathrm{check}\:\mathrm{the}\:\mathrm{question}…
Question Number 180467 by mathlove last updated on 12/Nov/22 Answered by cortano1 last updated on 12/Nov/22 Terms of Service Privacy Policy Contact: info@tinkutara.com