Question Number 132554 by mohammad17 last updated on 15/Feb/21 Commented by MJS_new last updated on 15/Feb/21 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{many}\:\mathrm{times}\:\mathrm{before}.\:\mathrm{simply} \\ $$$$\mathrm{substitute}\:{t}=\sqrt{\mathrm{tan}\:\theta}\:\mathrm{and}\:\mathrm{there}\:\mathrm{you}\:\mathrm{go} \\ $$ Commented by liberty last…
Question Number 67017 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 24/Aug/19 $${let}\:{I}\:=\int\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx}\:\:{changement}\:\sqrt{{x}+\mathrm{1}}={t}\:{give}\:{x}+\mathrm{1}={t}^{\mathrm{2}} \:\Rightarrow…
Question Number 67014 by mathmax by abdo last updated on 21/Aug/19 $${solve}\:{y}^{''} +{x}^{\mathrm{2}} {y}^{'} ={e}^{−{x}} {sin}\left(\mathrm{3}{x}\right) \\ $$ Commented by mathmax by abdo last updated…
Question Number 1479 by yyy last updated on 12/Aug/15 $$ \\ $$$$ \\ $$ Answered by 123456 last updated on 12/Aug/15 $$\xi:\mathbb{R}×\mathrm{X}\rightarrow\mathbb{R} \\ $$$$\xi_{\mathrm{X}} \left({s}\right)=\underset{{x}\in\mathrm{X}}…
Question Number 132548 by liberty last updated on 15/Feb/21 $$\mathrm{John}\:\mathrm{and}\:\mathrm{Ghina}\:\mathrm{have}\:\mathrm{a}\:\mathrm{date}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{given}\:\mathrm{time},\:\mathrm{and}\:\mathrm{each}\:\mathrm{will}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{meeting}\:\mathrm{place}\:\mathrm{with}\:\mathrm{a}\:\mathrm{delay}\:\mathrm{between} \\ $$$$\mathrm{0}\:\mathrm{and}\:\mathrm{1}\:\mathrm{hour},\:\mathrm{with}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of} \\ $$$$\mathrm{delays}\:\mathrm{being}\:\mathrm{equally}\:\mathrm{likely}. \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{arrive}\:\mathrm{will}\:\mathrm{wait}\:\mathrm{for} \\ $$$$\mathrm{15}\:\mathrm{minutes}\:\mathrm{and}\:\mathrm{will}\:\mathrm{leave}\:\mathrm{if} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{has}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{arrived}.\:\mathrm{What} \\…
Question Number 67015 by mathmax by abdo last updated on 21/Aug/19 $${let}\:{f}\left({x}\right)\:={arctan}\left(\mathrm{1}+{e}^{−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \right) \\ $$$${calculate}\:{f}^{'} \left({x}\right)\:\:{and}\:{f}^{''} \left({x}\right). \\ $$$$\left.\mathrm{1}\right){find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} \:\:\:{f}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){study}\:{the}\:{variation}\:{of}\:{f}\left({x}\right) \\…
Question Number 132551 by liberty last updated on 15/Feb/21 $$\mathrm{A}\:\mathrm{conservative}\:\mathrm{design}\:\mathrm{team}\:,\:\mathrm{call}\:\mathrm{it}\:\mathrm{C} \\ $$$$\mathrm{and}\:\mathrm{innovative}\:\mathrm{design}\:\mathrm{team}\:\mathrm{call} \\ $$$$\mathrm{it}\:\mathrm{N}\:,\:\mathrm{are}\:\mathrm{asked}\:\mathrm{to}\:\mathrm{separately}\:\mathrm{design} \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{product}\:\mathrm{within}\:\mathrm{a}\:\mathrm{month}. \\ $$$$\mathrm{From}\:\mathrm{past}\:\mathrm{experience}\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{C}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{is}\:\mathrm{2}/\mathrm{3} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{team}\:\mathrm{N}\:\mathrm{is}\:\mathrm{successful}\:\mathrm{1}/\mathrm{2} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\…
Question Number 67012 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{arctan}\left(\left[{x}\right]\right)}{{x}^{\mathrm{3}} }{dx} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 132550 by liberty last updated on 15/Feb/21 $$\mathrm{If}\:{a}=\mathrm{1}\:\mathrm{then}\:\underset{{x}\rightarrow\left({a}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{5}\right)} {\mathrm{lim}}\frac{−\mathrm{4}{x}^{\mathrm{2}} +\sqrt{\mathrm{3}{x}+\mathrm{1}}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{8}{x}}+\mathrm{2}}\:=? \\ $$$$\left(\mathrm{a}\right)\:−\mathrm{1}\:\:\:\:\:\:\:\left(\mathrm{b}\right)\:−\frac{\mathrm{4}}{\mathrm{5}}\:\:\:\:\:\:\:\left(\mathrm{c}\right)\:−\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$\left(\mathrm{d}\right)\:−\frac{\mathrm{2}}{\mathrm{5}}\:\:\:\:\left(\mathrm{e}\right)\:−\frac{\mathrm{1}}{\mathrm{5}} \\ $$ Commented by MJS_new last updated…
Question Number 67013 by mathmax by abdo last updated on 21/Aug/19 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right){n}^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…