Question Number 219090 by depressiveshrek last updated on 19/Apr/25 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sequence}\:{a}_{{n}} =\frac{\mathrm{1}}{\:\sqrt[{{n}}]{{n}!}}\:\mathrm{is}\:\mathrm{decreasing}. \\ $$ Answered by Frix last updated on 19/Apr/25 $${n}\rightarrow\infty\:\Rightarrow\:{n}!\approx\left(\frac{{n}}{\mathrm{e}}\right)^{{n}} \sqrt{\mathrm{2}\pi{n}}\:\Rightarrow \\ $$$$\frac{\mathrm{1}}{\:\sqrt[{{n}}]{{n}!}}\approx\frac{\mathrm{e}}{\left(\mathrm{2}\pi{x}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {x}}…
Question Number 218673 by Spillover last updated on 14/Apr/25 Commented by Nicholas666 last updated on 14/Apr/25 $$\varphi \\ $$ Answered by Nicholas666 last updated on…
Question Number 218311 by mr W last updated on 06/Apr/25 Answered by Frix last updated on 06/Apr/25 $${f}\left({x}\right)={c} \\ $$ Commented by mr W last…
Question Number 218256 by mr W last updated on 03/Apr/25 Answered by efronzo1 last updated on 03/Apr/25 $$\:\:\mathrm{f}\left(\mathrm{3}\right)+\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)=\:\mathrm{72} \\ $$$$\:\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)=−\mathrm{12} \\ $$$$\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)+\:\mathrm{f}\left(\mathrm{3}\right)\:=\:\mathrm{16} \\ $$$$\:\:\mathrm{2}\left\{\mathrm{f}\left(\mathrm{3}\right)+\:\mathrm{f}\left(−\frac{\mathrm{1}}{\mathrm{2}}\right)+\:\mathrm{f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)\right\}\:=\:\mathrm{76} \\…
Question Number 217725 by Spillover last updated on 19/Mar/25 Commented by ArshadS last updated on 20/Mar/25 $${MathematicalUser}!\:\:{if}\:“{you}\:{didn}'{t}\:{mean}\:{that}''\:{then} \\ $$$${why}\:{don}'{t}\:{you}\:{delete}\:{your}\:{comment}\:{and}\:{answer}? \\ $$ Commented by MathematicalUser2357 last…
Question Number 216077 by MATHEMATICSAM last updated on 27/Jan/25 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{non}\:\mathrm{negative} \\ $$$$\mathrm{integer}\:{p}\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left\{\frac{−\:{px}\:+\:\mathrm{sin}\left({x}\:−\:\mathrm{1}\right)\:+\:{p}}{{x}\:+\:\mathrm{sin}\left({x}\:−\:\mathrm{1}\right)\:−\:\mathrm{1}}\right\}^{\frac{\mathrm{1}\:−\:{x}}{\mathrm{1}\:−\:\sqrt{{x}}}} \:=\:\frac{\mathrm{1}}{\mathrm{4}}\:. \\ $$ Answered by mahdipoor last updated on 27/Jan/25…
Question Number 215887 by amoussou last updated on 20/Jan/25 Commented by mr W last updated on 20/Jan/25 $${please}\:{don}'{t}\:{repeat}\:{the}\:{same}\: \\ $$$${question}! \\ $$ Commented by Tawa11…
Question Number 215872 by amoussou last updated on 20/Jan/25 Commented by MathematicalUser2357 last updated on 20/Jan/25 Translate ??? Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 215331 by JasonHidd last updated on 03/Jan/25 Answered by mr W last updated on 03/Jan/25 $${f}\left({x}\right)\:{must}\:{be}\:{an}\:{odd}\:{integrable}\: \\ $$$${function},\:{i}.{e}. \\ $$$${f}\left(−{x}\right)=−{f}\left({x}\right) \\ $$$${e}.{g}.\: \\…
Question Number 214644 by asifumer658 last updated on 14/Dec/24 $$\frac{−\mathrm{6}}{\mathrm{7}}/\frac{−\mathrm{7}}{\mathrm{6}} \\ $$ Answered by Frix last updated on 17/Dec/24 $$\frac{−\mathrm{6}}{\mathrm{7}}/\frac{−\mathrm{7}}{\mathrm{6}}=\left(−\frac{\mathrm{6}}{\mathrm{7}}\right)/\left(−\frac{\mathrm{7}}{\mathrm{7}}\right)=\left(−\frac{\mathrm{6}}{\mathrm{7}}\right)×\left(−\frac{\mathrm{6}}{\mathrm{7}}\right)= \\ $$$$=\frac{\mathrm{36}}{\mathrm{49}} \\ $$ Terms…