Question Number 203693 by Numsey last updated on 26/Jan/24 Answered by MM42 last updated on 26/Jan/24 $${I}=\int\sqrt{\mathrm{2}}{cos}\frac{{x}}{\mathrm{2}}{dx}=\mathrm{2}\sqrt{\mathrm{2}}{sin}\frac{{x}}{\mathrm{2}}\:+{c} \\ $$ Commented by Frix last updated on…
Question Number 203726 by mr W last updated on 27/Jan/24 Commented by mr W last updated on 26/Jan/24 $${solution}\:{to}\:{Q}#\mathrm{203636} \\ $$ Answered by mr W…
Question Number 203694 by Numsey last updated on 26/Jan/24 Answered by Calculusboy last updated on 26/Jan/24 $$\boldsymbol{{Solution}}:\:\boldsymbol{{by}}\:\boldsymbol{{sub}}\:\boldsymbol{{directly}},\boldsymbol{{we}}\:\boldsymbol{{get}}\:\frac{\mathrm{0}}{\mathrm{0}}\left(\boldsymbol{{indeterminant}}\right) \\ $$$$\boldsymbol{{let}}\:\boldsymbol{\Delta}=\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\left(\mathrm{1}+\boldsymbol{{x}}\right)^{\mathrm{5}} }{\boldsymbol{{x}}^{\mathrm{2}} }−\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{e}}^{\mathrm{5}\boldsymbol{{x}}} }{\boldsymbol{{x}}^{\mathrm{2}} }+\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}}…
Question Number 203695 by Numsey last updated on 26/Jan/24 Commented by BaliramKumar last updated on 26/Jan/24 $$\mathrm{Step}\:\mathrm{III}\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{4}\left(\mathrm{27}\right)}\left(\mathrm{1}.\mathrm{5}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 203688 by ajfour last updated on 26/Jan/24 Commented by ajfour last updated on 26/Jan/24 $${Repost}\:\:\:{Q}.\mathrm{203636}\: \\ $$ Commented by ajfour last updated on…
Question Number 203690 by yaslm last updated on 26/Jan/24 Answered by Frix last updated on 26/Jan/24 $$=\frac{\mathrm{1}}{\mathrm{3}}\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}}−\frac{\mathrm{1}}{{x}+\mathrm{1}}{dx} \\ $$$$\mathrm{Should}\:\mathrm{be}\:\mathrm{easy}\:\mathrm{now} \\ $$ Terms of Service…
Question Number 203716 by professorleiciano last updated on 26/Jan/24 Answered by AST last updated on 26/Jan/24 $${Let}\:{AP}\:{and}\:{DC}\:{meet}\:{at}\:{F},{then}\:\bigtriangleup{BPA}\approx\bigtriangleup{CPF} \\ $$$$\Rightarrow\frac{{BA}}{{CF}}=\frac{{BP}}{{CP}}\Rightarrow\frac{{s}}{{CF}}=\frac{\mathrm{8}}{{s}−\mathrm{8}}\Rightarrow{CF}=\frac{{s}\left({s}−\mathrm{8}\right)}{\mathrm{8}}…\left({i}\right) \\ $$$${in}\:\bigtriangleup{AFD};{AQ}\:{bisects}\:\angle{FAD}\Rightarrow\frac{{AD}}{{DQ}}=\frac{{AF}}{{FQ}} \\ $$$$\Rightarrow\frac{{s}}{\mathrm{9}}=\frac{\sqrt{{s}^{\mathrm{2}} +\left({s}+{CF}\right)^{\mathrm{2}} }}{{CF}+{s}−\mathrm{9}}\Rightarrow\frac{{s}}{\mathrm{9}}=\frac{\sqrt{{s}^{\mathrm{2}}…
Question Number 203712 by Davidtim last updated on 26/Jan/24 $$\mathrm{50}\:{divide}\:{into}\:{to}\:{part}\:{that}\:{the}\:{mini}\: \\ $$$${figure}\:\frac{\mathrm{2}}{\mathrm{3}}\:{and}\:{large}\:{one}\:{is}\:\frac{\mathrm{5}}{\mathrm{7}},\:{and}\:{the}\: \\ $$$${sum}\:{of}\:{them}\:{is}\:\mathrm{21},\:{find}\:{the}\:{tow}\: \\ $$$${figures}? \\ $$ Commented by Davidtim last updated on 30/Jan/24…
Question Number 203714 by K1000 last updated on 26/Jan/24 $$\int\mathrm{2}{x}^{\mathrm{2}} \\ $$ Answered by Frix last updated on 26/Jan/24 $$\int{ax}^{{n}} {dx}={a}\int{x}^{{n}} {dx}=\frac{{ax}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}+{C} \\ $$…
Question Number 203676 by 073 last updated on 25/Jan/24 Answered by Frix last updated on 25/Jan/24 $${x}\left({x}+\mathrm{2}\right){x}!=\mathrm{168}{x}^{\mathrm{2}} \\ $$$${x}=\mathrm{0} \\ $$$$\left({x}+\mathrm{2}\right){x}!=\mathrm{168}{x} \\ $$$$\left({x}+\mathrm{2}\right)\left({x}−\mathrm{1}\right)!=\mathrm{168}=\mathrm{2}×\mathrm{3}×\mathrm{4}×\mathrm{7} \\ $$$${x}=\mathrm{5}…