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 $$\mathrm{this}\:\mathrm{is}\:\mathrm{not}\:\mathrm{possible},\:\mathrm{check}\:\mathrm{the}\:\mathrm{question}…
Question Number 180467 by mathlove last updated on 12/Nov/22 Answered by cortano1 last updated on 12/Nov/22 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 49326 by Saorey last updated on 05/Dec/18 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}! \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{1}} ={a},\:\mathrm{u}_{\mathrm{2}} =\mathrm{b}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{3}\sqrt[{\mathrm{5}}]{\mathrm{u}_{\mathrm{n}+\mathrm{1}} }+\mathrm{13}\sqrt[{\mathrm{5}}]{\mathrm{u}_{\mathrm{n}} }\:,\mathrm{n}\in\mathbb{N}^{\ast} }\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{u}_{\mathrm{n}} \right)\:\mathrm{have}\:\mathrm{limit}\:\mathrm{and}\:\mathrm{find}\: \\ $$$$\mathrm{its}\:\mathrm{limit}. \\ $$…
Question Number 180359 by mathlove last updated on 11/Nov/22 Answered by Frix last updated on 11/Nov/22 $$\mathrm{certainly}\:\mathrm{you}\:\mathrm{do}\:\mathrm{not}\:\mathrm{mean}\:{x}!\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{limit}\:\mathrm{exists} \\ $$$$\mathrm{but}\:\mathrm{you}\:\mathrm{mean}\:{x}!=\Gamma\left({x}+\mathrm{1}\right) \\ $$$$\mathrm{we}\:\mathrm{know}\:\Gamma\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\mathrm{let}\:\Gamma\left({x}+\mathrm{1}\right)={f}\left({x}\right)…
Question Number 114754 by bemath last updated on 21/Sep/20 $${Without}\:{L}'{Hopital}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\left(\frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:−\mathrm{2tan}\:{x}\:\right)}{\mathrm{cos}\:\mathrm{2}{x}}\:? \\ $$ Commented by bemath last updated on 21/Sep/20 $${gave}\:{kudos}\:{all}\:{sir} \\…
Question Number 114696 by bemath last updated on 20/Sep/20 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sinh}\:\left(\mathrm{2}{x}\right)−\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:=? \\ $$ Answered by bobhans last updated on 20/Sep/20 $${e}^{\mathrm{2}{x}} =\mathrm{1}+\mathrm{2}{x}+\mathrm{2}{x}^{\mathrm{2}} +\frac{\mathrm{4}{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{\mathrm{2}{x}^{\mathrm{4}}…
Question Number 114637 by bobhans last updated on 20/Sep/20 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\frac{\pi}{\mathrm{2}}−\mathrm{cos}\:^{−\mathrm{1}} \left(\mathrm{2}{x}−\pi\right)}{\mathrm{1}−\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}}{\pi}\right)}\:? \\ $$ Answered by bemath last updated on 20/Sep/20 $${setting}\:{x}=\frac{\pi}{\mathrm{2}}+{p}\rightarrow\mathrm{2}{x}=\pi+\mathrm{2}{p} \\ $$$$\underset{{p}\rightarrow\mathrm{0}}…