Question Number 213084 by MATHEMATICSAM last updated on 30/Oct/24 $$\mathrm{If}\:\mathrm{0}\:<\:{x}\:<\:\frac{\pi}{\mathrm{2}}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{sin}\left(\mathrm{cos}{x}\right)\:<\:\mathrm{cos}{x}\:<\:\mathrm{cos}\left(\mathrm{sin}{x}\right). \\ $$$$\mathrm{not}\:\mathrm{using}\:\mathrm{graph}. \\ $$ Answered by issac last updated on 30/Oct/24 $${x}=\mathrm{acos}\left({z}\right)\:,\:{z}\in\left[\mathrm{0},\mathrm{1}\right] \\…
Question Number 213119 by a.lgnaoui last updated on 30/Oct/24 $$\mathrm{determiner}\:\boldsymbol{\mathrm{a}}\:\mathrm{et}\:\boldsymbol{\mathrm{b}}\:\mathrm{par}\:\:\:;\:\:\mathrm{AB}\:\bot\mathrm{BC} \\ $$$$\begin{cases}{\mathrm{AM}\:=\mathrm{5}}\\{\mathrm{AC}\:\:=\mathrm{16}}\end{cases} \\ $$ Commented by a.lgnaoui last updated on 30/Oct/24 Answered by A5T last…
Question Number 213081 by issac last updated on 30/Oct/24 $$\mathrm{evaluate} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:\:\:\frac{\mathrm{tanh}\left(\frac{\mathrm{1}}{\mathrm{2}}{z}\right)\mathrm{csch}\left({z}\right)}{{z}}\mathrm{d}{z} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Complex}\:\mathrm{integral} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Feynman}\:\mathrm{trick} \\ $$ Answered by Berbere last updated…
Question Number 213114 by efronzo1 last updated on 30/Oct/24 $$\:\:\:\:\:\:\:\:\underline{\boldsymbol{\div}} \\ $$ Answered by issac last updated on 30/Oct/24 $$\:\:\:{f}\left({x}\right)=−{C}\left({x}−\mathrm{1}\right)+\frac{\boldsymbol{{i}}}{\pi}\left({x}−\mathrm{1}\right)^{\mathrm{5000}} \mathrm{ln}\left({x}−\mathrm{1}\right) \\ $$$$\left(\mathrm{thx}\:\mathrm{wolfram}\:\mathrm{alpha}!!\right) \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{0}\:,\:\mathrm{cus}\:\:{f}\left(\mathrm{1}+\mathrm{0}\right)+{f}\left(\mathrm{1}−\mathrm{0}\right)=\mathrm{0}^{\mathrm{5000}}…
Question Number 213082 by liuxinnan last updated on 30/Oct/24 Answered by MrGaster last updated on 30/Oct/24 $$\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{i}^{\frac{\mathrm{1}}{{n}}} \approx\int_{\mathrm{1}} ^{{n}} {x}^{\frac{\mathrm{1}}{{n}}} {dx} \\ $$$$\int{x}^{\frac{\mathrm{1}}{{x}}}…
Question Number 213109 by mathlove last updated on 30/Oct/24 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt{{x}+\sqrt{{x}+\sqrt{{x}}}}}{\:\sqrt{{x}+\mathrm{1}}}=? \\ $$ Answered by MrGaster last updated on 30/Oct/24 $$=\frac{\sqrt{{x}\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{x}}}+\frac{\mathrm{1}}{{x}}\right)}}{\:\sqrt{{x}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)}} \\ $$$$=\frac{\sqrt{{x}}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{x}}}+\frac{\mathrm{1}}{{x}}}}{\:\sqrt{{x}}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}}}} \\ $$$$=\frac{\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{x}}}+\frac{\mathrm{1}}{{x}}}}{\:\sqrt{\mathrm{1}+\frac{\mathrm{1}}{{x}}}}…
Question Number 213100 by MathematicalUser2357 last updated on 30/Oct/24 $$\mathrm{Find}\:\mathrm{this}\:\mathrm{numeric}\:\mathrm{expression}\:\mathrm{using}: \\ $$$$\mathrm{The}\:\mathrm{arithmetic}\:\mathrm{division}\:\mathrm{rule}\:{a}\boldsymbol{\div}{b}\left({c}\right)={a}\boldsymbol{\div}{b}×{c}, \\ $$$$\mathrm{The}\:\mathrm{solvable}\:\mathrm{incorrect}\:\mathrm{syntax}\:\mathrm{rule}\:\left({a}\right){b}={a}×{b},\:\mathrm{where}\:{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}: \\ $$$$\mathrm{12}\boldsymbol{\div}\mathrm{4}\left(\mathrm{10}−\mathrm{8}+\mathrm{1}\right)\mathrm{2}\boldsymbol{\div}\mathrm{6}×\mathrm{2}=? \\ $$ Commented by A5T last updated on 30/Oct/24…
Question Number 213103 by MathematicalUser2357 last updated on 30/Oct/24 $$\mathrm{Hey}\:\mathrm{tinku}\:\mathrm{tara}, \\ $$$$\mathrm{I}\:\mathrm{couldn}'\mathrm{t}\:\mathrm{graph}\:\mathrm{the}\:\mathrm{equation}. \\ $$ Commented by Tinku Tara last updated on 30/Oct/24 $$\mathrm{We}\:\mathrm{are}\:\mathrm{aware}\:\mathrm{of}\:\mathrm{the}\:\mathrm{issue}.\:\mathrm{Will}\:\mathrm{be} \\ $$$$\mathrm{fixed}\:\mathrm{in}\:\mathrm{coming}\:\mathrm{days}.…
Question Number 213128 by klipto last updated on 30/Oct/24 $$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}^{+\:} } \frac{\mathrm{2}}{\mathrm{1}+\boldsymbol{\mathrm{e}}^{−\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}} } \\ $$ Answered by a.lgnaoui last updated on 30/Oct/24 $$\boldsymbol{\mathrm{lim}}_{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}^{+\:} } \frac{\mathrm{2}}{\mathrm{1}+\boldsymbol{\mathrm{e}}^{−\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}}}…
Question Number 213096 by Tinku Tara last updated on 30/Oct/24 $$\mathrm{Hi}\:\mathrm{nikif90} \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{look}\:\mathrm{at}\:\mathrm{q212921}\:\mathrm{and} \\ $$$$\mathrm{provide}\:\mathrm{details}\:\mathrm{on}\:\mathrm{the}\:\mathrm{problem}\:\mathrm{that} \\ $$$$\mathrm{are}\:\mathrm{facimg} \\ $$ Answered by issac last updated on…