Question Number 132798 by metamorfose last updated on 16/Feb/21 $$\overset{\frac{\pi}{\mathrm{2}}} {\int}_{\mathrm{0}} \left(\sqrt{\mathrm{sin}\:\left({x}\right)}+\sqrt{\mathrm{cos}\:\left({x}\right)}\right){dx} \\ $$ Answered by Ñï= last updated on 17/Feb/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\sqrt{{sinx}}+\sqrt{{cosx}}\right){dx} \\…
Question Number 1724 by Hasan Mohamed last updated on 03/Sep/15 $$ \\ $$ Answered by 123456 last updated on 04/Sep/15 $${f}\left({x}\right)={x}!=\Gamma\left({x}+\mathrm{1}\right) \\ $$$${f}'\left({x}\right)={x}!\psi\left({x}+\mathrm{1}\right) \\ $$$$\psi\left({x}\right)=\frac{{d}}{{dx}}\mathrm{ln}\:\Gamma\left({x}\right)…
Question Number 67254 by TawaTawa last updated on 24/Aug/19 Commented by Rasheed.Sindhi last updated on 24/Aug/19 $$\:\:\:\:\:{Analytical}\:{Method} \\ $$$${x}-{axis}:{Horizanal}\:{Chord} \\ $$$${y}-{axis}:{Vertical}\:{Chord} \\ $$$${Three}\:{points}\:{on}\:{the}\:{circle}: \\ $$$$\:{A}\left(\mathrm{6},\mathrm{0}\right),{B}\left(−\mathrm{2},\mathrm{0}\right)\:\&\:{C}\left(\mathrm{0},−\mathrm{3}\right)…
Question Number 1716 by Rasheed Soomro last updated on 02/Sep/15 $${Determine}\:{interval}\:\boldsymbol{\mathrm{A}}\:{of}\:{real}\:{numbers}\:{for}\:{which} \\ $$$${a}^{{a}+\mathrm{1}} \geqslant\left({a}+\mathrm{1}\right)^{{a}} \:\:\:\:\:\:{whenever}\:{a}\in\boldsymbol{\mathrm{A}} \\ $$ Commented by Rasheed Ahmad last updated on 03/Sep/15…
Question Number 132785 by liberty last updated on 16/Feb/21 Commented by liberty last updated on 16/Feb/21 $$\:\mathrm{y}=\mathrm{ax}^{\mathrm{4}} +\mathrm{bx}^{\mathrm{3}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{e} \\ $$ Answered by MJS_new…
Question Number 67246 by Learner-123 last updated on 24/Aug/19 $${Integrate}: \\ $$$$\left.\mathrm{1}\right)\:\underset{\mathrm{3}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{1}/{x}\:{dx}}{{ln}\left({x}\right)\sqrt{{ln}^{\mathrm{2}} {x}−\mathrm{1}}} \\ $$$$\left.\mathrm{2}\right)\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{{e}^{{x}} {dx}}{\mathrm{1}+{e}^{\mathrm{2}{x}} } \\ $$$$\left.\mathrm{3}\right)\:\underset{\mathrm{1}} {\overset{\infty} {\int}}\:\frac{\mathrm{2}^{{x}}…
Question Number 67244 by Learner-123 last updated on 24/Aug/19 $${Which}\:{of}\:{the}\:{series}\:{converge}\:{and}\: \\ $$$${which}\:{diverge}?\:{Check}\:{by}\:{the}\:{limit} \\ $$$${comparison}\:{test}. \\ $$$$\left.\mathrm{1}\right)\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}+{n}\:{ln}\left({n}\right)}{{n}^{\mathrm{2}} +\mathrm{5}} \\ $$$$\left.\mathrm{2}\right)\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{ln}\left({n}\right)}{{n}^{\frac{\mathrm{3}}{\mathrm{2}}} } \\…
Question Number 67236 by prof Abdo imad last updated on 24/Aug/19 $${let}\:{T}_{{n}} ={cos}\left({narccosx}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculste}\:{T}_{\mathrm{0}} ,{T}_{\mathrm{1}} ,{T}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){find}\:\:{roots}\:{of}\:{T}_{{n}} \\ $$$$\left.\mathrm{3}\right){decompose}\:\:{the}\:{fraction}\:{F}\:=\frac{\mathrm{1}}{{T}_{{n}} } \\ $$ Commented…
Question Number 1700 by 112358 last updated on 01/Sep/15 $${Show}\:{that}\:\left(\mathrm{7}!\right)^{\frac{\mathrm{1}}{\mathrm{7}}} <\left(\mathrm{8}!\right)^{\frac{\mathrm{1}}{\mathrm{8}}} . \\ $$$${Also}\:{show}\:{that}\: \\ $$$$\sqrt{\mathrm{100001}}−\sqrt{\mathrm{100000}}<\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{100000}}}\:. \\ $$$$ \\ $$ Commented by 123456 last updated…
Question Number 67234 by prof Abdo imad last updated on 24/Aug/19 $${factorise}\:{p}\left({x}\right)=\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \:+{x}^{\mathrm{5}} \\ $$$${inside}\:{C}\left[{x}\right]\:{and}\:{R}\left[{x}\right] \\ $$$${calculate}\:{p}\left({e}^{{i}\frac{\pi}{\mathrm{5}}} \right)\:{and}\:{p}\left({cos}\left(\frac{\pi}{\mathrm{5}}\right)\right) \\ $$ Commented by mathmax by…