Question Number 191188 by cortano12 last updated on 20/Apr/23 $$\:\:\:\:\:\:\:\:\:\:\:\int\:\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−\mathrm{x}}{\mathrm{1}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Answered by mehdee42 last updated on 20/Apr/23 $$\sqrt[{\mathrm{4}}]{\frac{\mathrm{2}−{x}}{\mathrm{1}−{x}}}={u}\Rightarrow{x}=\frac{{u}^{\mathrm{4}} −\mathrm{2}}{{u}^{\mathrm{4}} −\mathrm{1}}\Rightarrow{dx}=\frac{\mathrm{4}{u}^{\mathrm{3}} }{\left({u}^{\mathrm{4}} −\mathrm{1}\right)^{\mathrm{2}} \:}\:{du}…
Question Number 191191 by mathlove last updated on 20/Apr/23 Answered by mehdee42 last updated on 20/Apr/23 $$\mathrm{14} \\ $$ Answered by mr W last updated…
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Question Number 60115 by cesar.marval.larez@gmail.com last updated on 17/May/19 Commented by mr W last updated on 18/May/19 Commented by cesar.marval.larez@gmail.com last updated on 18/May/19 $${thannks}\:{buddy}…
Question Number 125651 by Algoritm last updated on 12/Dec/20 Answered by Olaf last updated on 12/Dec/20 $$\begin{cases}{{y}_{\mathrm{1}} '\:=\:{y}_{\mathrm{1}} +\mathrm{4}{y}_{\mathrm{2}} \:\left(\mathrm{1}\right)}\\{{y}_{\mathrm{2}} '\:=\:−{y}_{\mathrm{1}} +{y}_{\mathrm{2}} +{e}^{\mathrm{3}{x}} \:\left(\mathrm{2}\right)}\end{cases} \\…
Question Number 191187 by mathlove last updated on 20/Apr/23 $${prove}\:{that} \\ $$$$\mathrm{1}:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{tanx}}{{x}^{\mathrm{3}} }=\frac{−\mathrm{1}}{\mathrm{3}} \\ $$$$\mathrm{2}:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{3}} }=\frac{\mathrm{1}}{\mathrm{3}} \\ $$ Commented by mathlove last…
Question Number 125649 by bramlexs22 last updated on 12/Dec/20 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}\:\mathrm{arc}\:\mathrm{tan}\:{x}\right)+\mathrm{1}−{e}^{{x}} }{\:\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{4}} }\:−\mathrm{1}}\:?\: \\ $$ Answered by Olaf last updated on 13/Dec/20 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\frac{\mathrm{ln}\left(\mathrm{1}+{x}\mathrm{arctan}{x}\right)+\mathrm{1}−{e}^{{x}} }{\:\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{4}} }−\mathrm{1}}…
Question Number 125645 by aurpeyz last updated on 12/Dec/20 $${In}\:{a}\:{certain}\:{set}\:{of}\:\mathrm{200}\:{students}.\: \\ $$$${subset}\:{A}\:{are}\:{blondes}\:{and}\:{the}\:{rest}\:{are} \\ $$$${brunettes}.\:{B}\:{are}\:{left}\:{handed}.\:{and}\: \\ $$$${C}\:{are}\:{left}−{handed}\:{blondes}. \\ $$$$ \\ $$$$\left(\mathrm{1}\right){Express}\:{in}\:{terms}\:{of}\:{A}\:{B}\:{C}\:{the}\: \\ $$$${subset}\:{consisting}\:{of}\:{right}−{handed} \\ $$$${brunettes}. \\…
Question Number 191177 by naka3546 last updated on 19/Apr/23 $$\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{coefficient}\:\:\mathrm{of}\:\:{x}^{\mathrm{18}\:} \:\:\mathrm{in}\:\:\mathrm{expression}\:\: \\ $$$$\left(\mathrm{1}+\:{x}^{\mathrm{3}} \:+\:{x}^{\mathrm{5}} \:+\:{x}^{\mathrm{7}} \right)^{\mathrm{100}} \:\:. \\ $$ Answered by mehdee42 last updated on…