Question Number 69255 by TawaTawa last updated on 21/Sep/19 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\:\sqrt{\frac{\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{4}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{3x}\:+\:\mathrm{2}}} \\ $$ Answered by Henri Boucatchou last updated on 21/Sep/19 $$\underset{\boldsymbol{{x}}\rightarrow\mathrm{2}} {\boldsymbol{{lim}}}\sqrt{\frac{\boldsymbol{{x}}^{\mathrm{3}}…
Question Number 134760 by rs4089 last updated on 07/Mar/21 Answered by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\left[\frac{\left(\mathrm{n}!\right)}{\mathrm{n}}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} \:\Rightarrow\mathrm{U}_{\mathrm{n}} =\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{n}}\mathrm{log}\left(\frac{\mathrm{n}!}{\mathrm{n}}\right)} \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{n}!\sim\mathrm{n}^{\mathrm{n}} \mathrm{e}^{−\mathrm{n}}…
Question Number 69212 by aliesam last updated on 21/Sep/19 $${use}\:{limit}\:{comparison}\:{test}\:{to}\:{determine} \\ $$$${the}\:{series}\:{converge}\:{or}\:{diverge} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}{ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{k}^{\mathrm{2}} }\right) \\ $$ Answered by mind is power last…
Question Number 134741 by zahaku last updated on 06/Mar/21 $$\underset{\rightarrow−\mathrm{3}} {{lim}}\frac{{x}+\mathrm{3}}{\:\sqrt{\mid{x}^{\mathrm{2}} +{x}−\mathrm{6}\mid}}\:\:? \\ $$ Answered by mathmax by abdo last updated on 07/Mar/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{x}+\mathrm{3}}{\:\sqrt{\mid\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{6}\mid}}\:\mathrm{changement}\:\mathrm{x}+\mathrm{3}=\mathrm{t}\:\mathrm{give}…
Question Number 134746 by zahaku last updated on 06/Mar/21 $${How}\:{to}\:{calculate} \\ $$$${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{{x}+\mathrm{3}}{\:\sqrt{\mid{x}^{\mathrm{2}} +{x}−\mathrm{6}\mid}}\:\:\:\:? \\ $$ Answered by mathmax by abdo last updated on 06/Mar/21…
Question Number 69174 by Aditya789 last updated on 21/Sep/19 $${find}\:{the}\:{value}\:{of}\: \\ $$$${lim}\frac{\mathrm{1}+{cosx}}{{tan}^{\mathrm{2}{x}} } \\ $$$${x}\hat {−}\upuparrows \\ $$ Commented by Henri Boucatchou last updated on…
Question Number 134665 by EDWIN88 last updated on 06/Mar/21 $$\mathscr{N}\:=\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:+\:\sqrt{\mathrm{x}−\mathrm{1}}}{\:\sqrt{\mathrm{x}^{\mathrm{3}} −\mathrm{1}}}\:=? \\ $$ Answered by benjo_mathlover last updated on 06/Mar/21 $$\mathscr{N}\:=\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}−\mathrm{1}}\:\left\{\sqrt{\mathrm{x}+\mathrm{1}}+\mathrm{1}\:\right\}}{\:\sqrt{\mathrm{x}−\mathrm{1}}\:\left\{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\:\right\}}…
Question Number 3546 by prakash jain last updated on 15/Dec/15 $$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{p}_{{i}} },\:{p}_{{i}} \:{is}\:{i}^{{th}} \:{prime}\:{diverges}. \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{s}_{{i}} },\:{s}_{{i}} \:{is}\:{i}^{{th}} \:{whole}\:{square}\:{converges}. \\ $$$$\mathrm{Why}?…
Question Number 69074 by Aditya789 last updated on 19/Sep/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 69075 by Aditya789 last updated on 19/Sep/19 Commented by Prithwish sen last updated on 19/Sep/19 $$\mathrm{Divide}\:\mathrm{both}\:\mathrm{numerator}\:\mathrm{and}\:\mathrm{denominator} \\ $$$$\mathrm{by}\:\mathrm{x}^{\mathrm{3}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{will}\:\mathrm{be}\:\mathrm{1} \\ $$ Commented by…