Question Number 226550 by gregori last updated on 03/Dec/25 $$\:\:\:\: {a}+{b}+{c}\:=\:{x}\: \\ $$$$\:\:\:\: \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} }{{abc}}\:=? \\ $$ Answered by peace2 last updated…
Question Number 224713 by efronzo1 last updated on 28/Sep/25 $$\:\:\:\cancel{\underline{\underbrace{\boldsymbol{{x}}}}} \\ $$ Answered by mehdee7396 last updated on 29/Sep/25 $$\mathrm{1} \\ $$ Commented by gregori…
Question Number 224288 by mnjuly1970 last updated on 31/Aug/25 $$ \\ $$$$\:\:\:\:\:\:\mathrm{P}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{k}}}\:\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}{k}}\right)}\:=?\:\:\:\: \\ $$$$ \\ $$ Commented by Frix last updated on 31/Aug/25…
Question Number 223990 by RoseAli last updated on 12/Aug/25 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}\left({x}+\frac{\mathrm{1}}{{x}}\right)^{\mathrm{5}} −\mathrm{32}\:}{{x}−\mathrm{1}} \\ $$ Commented by prathita last updated on 12/Aug/25 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}} \\ $$…
Question Number 223193 by Tawa11 last updated on 17/Jul/25 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{r}\:\mathrm{sin}\:\theta\right)\:\mathrm{d}\theta\:\:\:=\:\:\:\mathrm{2}\boldsymbol{\chi}_{\mathrm{2}} \left(\frac{\sqrt{\mathrm{1}\:\:+\:\:\mathrm{r}^{\mathrm{2}} }\:\:−\:\:\mathrm{1}}{\mathrm{r}}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 223082 by DarthMath last updated on 14/Jul/25 $${if}\:\underset{{x}\rightarrow+\infty} {{lim}x}−{f}\left({x}\right)=+\infty\:{and}\:\underset{{x}\rightarrow+\infty} {{lim}x}+{f}\left({x}\right)=+\infty \\ $$$${can}\:{we}\:{determine}\:\underset{{x}\rightarrow+\infty} {{lim}}\frac{{x}−{f}\left({x}\right)}{{x}+{f}\left({x}\right)} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 222756 by Osefavour last updated on 06/Jul/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\sqrt{\boldsymbol{\mathrm{cos}}\left(\boldsymbol{\mathrm{x}}\right)}}{\:\boldsymbol{\mathrm{x}}−\boldsymbol{\mathrm{xcos}}\left(\sqrt{\boldsymbol{\mathrm{x}}}\right)} \\ $$ Answered by gregori last updated on 07/Jul/25 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}}{{x}\left(\mathrm{1}−\mathrm{cos}\:\sqrt{{x}}\:\right)\left(\mathrm{1}+\sqrt{\mathrm{cos}\:{x}}\right)} \\ $$$$\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 222478 by mnjuly1970 last updated on 28/Jun/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \frac{{H}_{{n}} }{{n}^{\mathrm{2}} }\:=\:? \\ $$$$\:{note}:\:\:\:{H}_{{n}} =\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+…+\frac{\mathrm{1}}{{n}}\: \\ $$ Answered by MrGaster…
Question Number 222261 by MathematicalUser2357 last updated on 21/Jun/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}\left({x}^{\mathrm{2}} +\mathrm{4}{x}\right)}{\mathrm{sin}\left(\mathrm{9}{x}^{\mathrm{2}} +{x}\right)} \\ $$$$\mathrm{No}\:\mathrm{L}'\mathrm{h}\hat {\mathrm{o}pital}'\mathrm{s}\:\mathrm{rule}\:\mathrm{allowed}! \\ $$ Answered by gregori last updated on 21/Jun/25…
Question Number 221392 by Davidtim last updated on 02/Jun/25 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\sqrt{{x}−\mathrm{3}}=? \\ $$$$\left.\mathrm{1}\right)\:\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{3} \\ $$$$\left.\mathrm{3}\right)\:{Does}\:{not}\:{exist} \\ $$$$\left.\mathrm{4}\right)\:{Undefined} \\ $$ Answered by Frix last…