Question Number 206869 by universe last updated on 28/Apr/24 Commented by Frix last updated on 28/Apr/24 $$\mathrm{Answer}\:\mathrm{is}\:\mathrm{e}^{{a}_{\mathrm{1}} } −\mathrm{1}\:\mathrm{for}\:{a}_{\mathrm{1}} \in\mathbb{R}\backslash\left\{\mathrm{0}\right\} \\ $$ Commented by universe…
Question Number 206845 by hardmath last updated on 27/Apr/24 $$\mathrm{Find}:\:\:\:\frac{\infty!}{\infty^{\infty} }\:=\:? \\ $$ Commented by A5T last updated on 27/Apr/24 $${Do}\:{you}\:{wish}\:{to}\:{find}\:{this}:\:\underset{{n}\rightarrow\infty} {{lim}}\frac{{n}!}{{n}^{{n}} }\:? \\ $$…
Question Number 206829 by 2kdw last updated on 27/Apr/24 $$\:\:\:\:\:\oint\frac{{x}}{{x}+\mathrm{2}}{dx}^{\mathrm{2}} \:\:\:\:{is}\:{wrong}? \\ $$ Commented by mr W last updated on 27/Apr/24 $${there}\:{are}\:{things}\:{to}\:{which}\:{you}\:{can} \\ $$$${say}\:{they}\:{are}\:{wrong},\:{for}\:{example} \\…
Question Number 206830 by Fabricista15 last updated on 27/Apr/24 $${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}}…
Question Number 206858 by Ghisom last updated on 27/Apr/24 $$\mathrm{prove}\:\mathrm{that} \\ $$$${H}_{{n}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{n}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$ Answered by mathzup last updated on 28/Apr/24…
Question Number 206827 by Fabricista15 last updated on 27/Apr/24 $$\mathrm{log}\:\left({x}\right)\:=\:\mathrm{sin}\:\left({x}\right) \\ $$$${x}\:=\:? \\ $$ Commented by Ghisom last updated on 27/Apr/24 $$\mathrm{if}\:\mathrm{log}\:{x}\:=\mathrm{ln}\:{x}\:\Rightarrow \\ $$$$\:\:\:\:\:{x}\approx\mathrm{2}.\mathrm{21910715} \\…
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Question Number 206839 by efronzo1 last updated on 27/Apr/24 Answered by A5T last updated on 27/Apr/24 $${k}^{\mathrm{3}} +{k}^{\mathrm{2}} +\mathrm{2}{k}+\mathrm{2}\leqslant{k}^{\mathrm{2}} +{k}+\mathrm{300}\Leftrightarrow{k}^{\mathrm{3}} +{k}\leqslant\mathrm{298} \\ $$$$\Rightarrow\mathrm{0}\leqslant{k}\leqslant\mathrm{6};\:{checking}\:{implies}\:{k}=\mathrm{0}\:{or}\:\mathrm{2}. \\ $$$${So},{sum}=\mathrm{2}…
Question Number 206848 by BaliramKumar last updated on 27/Apr/24 Commented by BaliramKumar last updated on 27/Apr/24 Answered by A5T last updated on 27/Apr/24 $${Let}\:{side}\:{of}\:{square}={s} \\…