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…
Question Number 213097 by issac last updated on 30/Oct/24 $$\mathrm{Uhhhh}. \\ $$$$\mathrm{can}\:\mathrm{you}\:\mathrm{guys}\:\mathrm{solve}\:\mathrm{Partial}\:\mathrm{differantial}\:\mathrm{equation} \\ $$$$\bigtriangledown^{\mathrm{2}} \boldsymbol{\phi}=\mathrm{0} \\ $$$$\mathrm{Cylinderical}\:\mathrm{Laplacian}\:\mathrm{case} \\ $$$$\bigtriangledown^{\mathrm{2}} =\frac{\mathrm{1}}{\rho}\centerdot\frac{\partial\:\:}{\partial\rho}\left(\rho\frac{\partial\:\:}{\partial\rho}\right)+\left(\frac{\mathrm{1}}{\rho}\right)^{\mathrm{2}} \frac{\partial^{\mathrm{2}} \:}{\partial\phi^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} \:\:}{\partial{z}^{\mathrm{2}} }…
Question Number 213098 by MathematicalUser2357 last updated on 30/Oct/24 $$\int\frac{\mathrm{3}{x}+\mathrm{2}}{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}\mathrm{d}{x}=? \\ $$ Answered by issac last updated on 30/Oct/24 $$\mathrm{Hmmmmm}….. \\ $$$$\frac{\mathrm{3}{x}+\mathrm{2}}{\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}=\frac{\mathrm{3}\left(\mathrm{10}{x}+\mathrm{2}\right)}{\mathrm{10}\left(\mathrm{5}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}\right)}+\frac{\mathrm{7}}{\mathrm{5}\left(\mathrm{5}{x}^{\mathrm{2}}…
Question Number 213099 by MathematicalUser2357 last updated on 30/Oct/24 $$\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}\right)−\left({x}−\mathrm{3}\right)=\frac{\mathrm{1}}{\mathrm{3}}\left({x}+\mathrm{3}\right)+\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${x}=… \\ $$ Answered by MrGaster last updated on 30/Oct/24 $$\frac{\mathrm{1}}{\mathrm{2}}{x}−\frac{\mathrm{1}}{\mathrm{2}}−{x}+\mathrm{3}=\frac{\mathrm{1}}{\mathrm{3}}{x}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}{x}+\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{7}}{\mathrm{6}} \\…
Question Number 213123 by a.lgnaoui last updated on 30/Oct/24 $$\mathrm{factoriser} \\ $$$$\boldsymbol{\mathrm{x}}^{\mathrm{5}} +\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{\mathrm{x}}−\mathrm{1} \\ $$ Answered by MrGaster last updated on 30/Oct/24 $$\left({x}^{\mathrm{5}}…