Question Number 6991 by Tawakalitu. last updated on 05/Aug/16 $${Solve}:\:\:\left(\mathrm{1}\:−\:{x}^{\mathrm{2}} \right)\:\frac{{dy}}{{dx}}\:+\:{xy}\:=\:{xp} \\ $$$$ \\ $$$$ \\ $$ Answered by Yozzii last updated on 05/Aug/16 $${x}\neq\mathrm{1}:\:{y}'+\frac{{x}}{\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 138060 by mathocean1 last updated on 09/Apr/21 $${We}\:{throw}\:\mathrm{2}\:{times}\:{a}\:{cubic}\:{dice}\:.\:{Its} \\ $$$${faces}\:{are}\:{numeroted}\:\mathrm{0},\:\mathrm{0},\:−\mathrm{1},\:\mathrm{1},\mathrm{1},\mathrm{1}. \\ $$$${We}\:{note}\:{a}\:{the}\:{result}\:{of}\:{the}\:{face}\:{throw} \\ $$$${and}\:{b}\:{the}\:{result}\:{of}\:{second}\:{one}.\: \\ $$$$\left.\mathrm{1}\right){Calculate}\:{the}\:{probabilities}\:{to}\:{have}\: \\ $$$${a}\:{and}\:{b}\:{which}\:{verify}\:: \\ $$$$\bullet{a}=−\mathrm{1}\:{and}\:{b}=\mathrm{0} \\ $$$$\bullet{a}=\mathrm{1}\:{and}\:{b}=\mathrm{0} \\…
Question Number 6990 by Tawakalitu. last updated on 04/Aug/16 Answered by sou1618 last updated on 05/Aug/16 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({x}\right)^{\mathrm{1}/{x}} \\ $$$${ln}\left({L}\right)=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}}{ln}\left({x}\right) \\ $$$${when}\:\mathrm{0}<{x} \\ $$$$\:\:\:\:\mathrm{0}<\frac{\mathrm{1}}{{x}},…
Question Number 138062 by I want to learn more last updated on 09/Apr/21 Answered by mr W last updated on 09/Apr/21 $$\left({i}\right) \\ $$$$\left({a}\right) \\…
Question Number 6987 by sarathon last updated on 04/Aug/16 $${why}\:\:{e}^{{ln}\frac{\mathrm{1}}{\mathrm{3}}} \:{to}\:{be}\:\frac{\mathrm{1}}{\mathrm{3}}??? \\ $$$$ \\ $$$$ \\ $$ Commented by FilupSmith last updated on 04/Aug/16 $${a}^{\mathrm{log}_{{a}}…
Question Number 138059 by sahnaz last updated on 09/Apr/21 $$\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}} +\:\mathrm{3}^{\mathrm{n}+\mathrm{2}} +\:\mathrm{4}^{\mathrm{n}+\mathrm{3}} }{\mathrm{2}^{\mathrm{n}} +\mathrm{3}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}} }=? \\ $$ Answered by MJS_new last updated on 10/Apr/21…
Question Number 6983 by FilupSmith last updated on 04/Aug/16 $${I}=\int_{\mathrm{0}} ^{\:{a}} \left(\mathrm{1}+\frac{{n}}{{x}}\right)^{{x}} {dx} \\ $$$${I}=? \\ $$ Commented by FilupSmith last updated on 04/Aug/16 $$\mathrm{Current}\:\mathrm{working}…
Question Number 72519 by ajfour last updated on 29/Oct/19 Commented by ajfour last updated on 29/Oct/19 $${I}\:{mean}\:{with}\:{the}\:{stone}\:{in}\:{the}\:{hand}, \\ $$$${giving}\:{it}\:{the}\:{minimum}\:{velocity}. \\ $$ Answered by mr W…
Question Number 6982 by FilupSmith last updated on 04/Aug/16 $${n}={p}^{{n}} −{pn} \\ $$$${n}=? \\ $$ Commented by sou1618 last updated on 05/Aug/16 $${if}\:\:{n}\in\mathbb{N}…. \\ $$$${n}={p}\left({p}^{{n}−\mathrm{1}}…
Question Number 6979 by Fitrah A last updated on 04/Aug/16 $$\underset{\mathrm{0}} {\overset{\pi} {\int}}\left({sin}\:\mathrm{3}{x}\:+\:{cos}\:{x}\right)\:{dx}\:=\:? \\ $$ Answered by sandy_suhendra last updated on 04/Aug/16 $$=\left[−\frac{\mathrm{1}}{\mathrm{3}}{cos}\:\mathrm{3}{x}\:+\:{sin}\:{x}\right]_{\mathrm{0}} ^{\pi} \\…