Question Number 157191 by naka3546 last updated on 20/Oct/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:{x}\:−\:{x}\:+\:\frac{\mathrm{1}}{\mathrm{6}}\:{x}^{\mathrm{3}} }{{x}^{\mathrm{5}} }\:\:\:=\:\:? \\ $$$$\left(\:{Without}\:\:{L}'{Hospital}\:,\:{Taylor}\:\:{or}\:\:{Maclaurin}\:\:{Series}\:\right)\:. \\ $$ Answered by puissant last updated on 20/Oct/21 $${We}\:{have}\:{x}−\frac{{x}^{\mathrm{3}}…
Question Number 157177 by mathocean1 last updated on 20/Oct/21 Answered by puissant last updated on 20/Oct/21 Commented by mathocean1 last updated on 22/Oct/21 $${thanks}\:{le}\:{puissant}. \\…
Question Number 157168 by mathocean1 last updated on 20/Oct/21 $${x}\:,\:{y}\:{and}\:{z}\:{are}\:{numbers}. \\ $$$${Show}\:{that}\:{max}\left({x},\:{y}\right)=\frac{{x}+{y}+\mid{x}−{y}\mid}{\mathrm{2}}\:{and}\:{min}\left({x},{y}\right)=\frac{{x}+{y}−\mid{x}−{y}\mid}{\mathrm{2}} \\ $$$${then}\:{find}\:{a}\:{formula}\:{for}\: \\ $$$${max}\left({x},{y},{z}\right). \\ $$ Answered by puissant last updated on 20/Oct/21…
Question Number 157171 by mathocean1 last updated on 20/Oct/21 $${calculate}\:\underset{{n}\rightarrow+\infty} {{lim}}\left(\frac{{n}+{ln}\left({n}\right)+\mathrm{1}}{\left(\mathrm{5}+\sqrt{{n}}\right)^{\mathrm{2}} }\right) \\ $$ Answered by puissant last updated on 20/Oct/21 $$\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{n}+{ln}\left({n}\right)+\mathrm{1}}{\left(\mathrm{5}+\sqrt{{n}}\right)^{\mathrm{2}} }\right)=\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{n}\left(\mathrm{1}+\frac{{ln}\left({n}\right)}{{n}}+\frac{\mathrm{1}}{{n}}\right)}{{n}\left(\frac{\mathrm{5}}{\:\sqrt{{n}}}+\mathrm{1}\right)^{\mathrm{2}}…
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Question Number 91622 by Ar Brandon last updated on 02/May/20 $$\frac{\mathrm{d}\left(\mathrm{x}!\right)}{\mathrm{dx}}= \\ $$ Commented by MJS last updated on 02/May/20 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{several}\:\mathrm{times}\:\mathrm{before} \\ $$$${x}!\:\mathrm{is}\:\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{N}\:\Rightarrow\:\mathrm{no}\:\mathrm{derivate}\:\mathrm{exists} \\ $$$$\mathrm{if}\:\mathrm{you}\:\mathrm{mean}\:\Gamma\left({x}\right)\:\mathrm{you}\:\mathrm{must}\:\mathrm{say}\:\mathrm{it}……
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Question Number 91595 by mahdi last updated on 01/May/20 $$\mathrm{what}'\mathrm{s}\:\mathrm{meaning}\:\mathrm{of}\:\left(\overset{.} {\mathrm{x}}\right)\:\mathrm{or}\:\left(\overset{..} {\mathrm{x}}\right)? \\ $$$$\mathrm{are}\:\left(\overset{.} {\mathrm{x}}\right)=\mathrm{x}'? \\ $$ Commented by mr W last updated on 01/May/20…
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Question Number 157104 by zakirullah last updated on 19/Oct/21 $${prove}\:\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\bigtriangleup{x}} −\mathrm{1}}{\bigtriangleup{x}}=\mathrm{1} \\ $$ Answered by puissant last updated on 19/Oct/21 $$\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\Delta{x}} −\mathrm{1}}{\Delta{x}}\:\sim\underset{\Delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}+\Delta{x}−\mathrm{1}}{\Delta{x}}=\mathrm{1}…