Question Number 131965 by liberty last updated on 10/Feb/21 Commented by liberty last updated on 10/Feb/21 Commented by TheSupreme last updated on 10/Feb/21 $${T}={t}_{\mathrm{1}} +{t}_{\mathrm{2}}…
Question Number 131960 by liberty last updated on 10/Feb/21 Answered by mr W last updated on 10/Feb/21 $${r}^{\mathrm{2}} +{h}^{\mathrm{2}} =\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} \:\Rightarrow{r}^{\mathrm{2}} =\mathrm{3}−{h}^{\mathrm{2}} \\ $$$${V}=\frac{\pi}{\mathrm{3}}{r}^{\mathrm{2}} {h}=\frac{\pi}{\mathrm{3}}\left(\mathrm{3}−{h}^{\mathrm{2}}…
Question Number 131887 by Algoritm last updated on 09/Feb/21 Answered by SEKRET last updated on 09/Feb/21 $$\:\boldsymbol{\mathrm{Leybnist}}\:\:\:\boldsymbol{\mathrm{formula}} \\ $$$$\:\:\boldsymbol{\mathrm{u}}=\:\boldsymbol{\mathrm{e}}^{−\mathrm{2}\boldsymbol{\mathrm{x}}} \:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{u}}^{\boldsymbol{\mathrm{n}}} =\left(−\mathrm{2}\right)^{\boldsymbol{\mathrm{n}}} \centerdot\boldsymbol{\mathrm{e}}^{−\mathrm{2}\boldsymbol{\mathrm{x}}} \\ $$$$\:\boldsymbol{\mathrm{v}}=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}}}\:\:\:\:\:\:\boldsymbol{\mathrm{v}}^{\boldsymbol{\mathrm{n}}} =\frac{\left(\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}\right)!!}{\mathrm{2}^{\boldsymbol{\mathrm{n}}}…
Question Number 131827 by Salman_Abir last updated on 09/Feb/21 Answered by liberty last updated on 09/Feb/21 $$\left.\:=\:\mathrm{ln}\:\mid\mathrm{tan}\:\mathrm{x}\mid\:\right]_{\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{3}}} \:=\:\mathrm{ln}\:\mid\mathrm{tan}\:\frac{\pi}{\mathrm{3}}\mid−\mathrm{ln}\:\mid\mathrm{tan}\:\frac{\pi}{\mathrm{4}}\mid \\ $$$$\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ln}\:\left(\mathrm{3}\right) \\ $$ Terms of…
Question Number 66256 by Mikael last updated on 11/Aug/19 $${Find}\:{all}\:{points}\:\left({a},\:{b}\right)\:{of}\:\mathbb{R}^{\mathrm{2}} \:{such}\:{that}\: \\ $$$${through}\:\left({a},\:{b}\right)\:{pass}\:{two}\:{tangent}\:{lines} \\ $$$${to}\:{the}\:{graph}\:{of}\:{f}\left({x}\right)={x}^{\mathrm{2}} . \\ $$ Commented by kaivan.ahmadi last updated on 11/Aug/19…
Question Number 131775 by Raxreedoroid last updated on 08/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of} \\ $$$${g}\left({x}\right)=\int_{\mathrm{tan}\:{x}} ^{\:{x}^{\mathrm{2}} } \frac{\mathrm{1}}{\:\sqrt{\mathrm{2}+{t}^{\mathrm{4}} }}\:{dt} \\ $$ Answered by bemath last updated on 08/Feb/21…
Question Number 131732 by mnjuly1970 last updated on 07/Feb/21 $$\:\:\:{prove}\:{that}: \\ $$$$\:\: \\ $$$$\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}−\mathrm{1}\right)\left({e}^{\left(\mathrm{2}{n}−\mathrm{1}\right)\pi} −{e}^{−\left(\mathrm{2}{n}−\mathrm{1}\right)\pi} \right)}=\frac{{ln}\left(\mathrm{2}\right)}{\mathrm{16}} \\ $$$$\: \\ $$ Terms of Service…
Question Number 131733 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{minimum}}\:\boldsymbol{{distance}} \\ $$$$\boldsymbol{{between}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:\left(\mathrm{1},\mathrm{1},\mathrm{1}\right)\:{and} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{plane}}\:\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{y}}+\mathrm{3}\boldsymbol{{z}}=\mathrm{6} \\ $$$$ \\ $$ Answered by physicstutes last updated on 07/Feb/21…
Question Number 131734 by LYKA last updated on 07/Feb/21 $$\boldsymbol{{given}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)=\boldsymbol{{xy}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{y}}−\mathrm{1}\right) \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{f}}\left(\boldsymbol{{x}}.\boldsymbol{{y}}\right)\:\boldsymbol{{has}}\:\boldsymbol{{some}}\:\left(\mathrm{0},\mathrm{1}\right) \\ $$$$\boldsymbol{{as}}\:\boldsymbol{{a}}\:\boldsymbol{{stationery}}\:\boldsymbol{{point}} \\ $$$$ \\ $$$$\boldsymbol{{use}}\:\boldsymbol{{tylor}}\:\boldsymbol{{series}}\:\boldsymbol{{method}}\:\boldsymbol{{to}}\: \\ $$$$\boldsymbol{{determine}}\:\boldsymbol{{whether}}\:\left(\mathrm{0}.\mathrm{1}\right)\:\boldsymbol{{is}}\:\boldsymbol{{a}} \\ $$$$\boldsymbol{{minima}}\:,\boldsymbol{{maxima}}\:\boldsymbol{{or}}\:\boldsymbol{{saddle}}\: \\…
Question Number 131735 by LYKA last updated on 07/Feb/21 $${calculate}\:{the}\:{k}-{th}\:{order}\:{Taylor} \\ $$$${polynomials}\:{T}_{{p}} ^{{k}} {f}\:{for}\:{the}\:{following} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{{e}^{−{x}} }{\mathrm{1}+{x}}\:\:\:{for}\:{p}=−\mathrm{1}\:{and}\:{k}=\mathrm{5} \\ $$$$ \\ $$$${f}\left({x}.{y}\right)=\:\mathrm{4}{sin}\left({x}^{\mathrm{2}} +{y}\right)\:{for}\:{p}=\left(\mathrm{0},\mathrm{0}\right)\:{and} \\…