Question Number 2435 by Yozzi last updated on 20/Nov/15 $${Prove}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Gamma'\left(\mathrm{1}\right)=\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {lnxdx} \\ $$$${is}\:{a}\:{negative}\:{number}. \\ $$ Commented by prakash jain last updated…
Question Number 2434 by Yozzi last updated on 20/Nov/15 $${Prove}\:{that}\:{for}\:{m}=\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{x}\rightarrow−{m}} {\mathrm{lim}}\Gamma\left({x}\right)=\infty. \\ $$ Answered by 123456 last updated on 25/Nov/15 $$\Gamma\left({x}+\mathrm{1}\right)={x}\Gamma\left({x}\right) \\ $$$$\mathrm{so}…
Question Number 67969 by behi83417@gmail.com last updated on 02/Sep/19 $$\boldsymbol{\mathrm{Two}}\:\boldsymbol{\mathrm{triangles}}\:\bigtriangleup_{\mathrm{1}} \:\boldsymbol{\mathrm{and}}\:\bigtriangleup_{\mathrm{2}} \:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{given}},\boldsymbol{\mathrm{such}}\: \\ $$$$\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{sides}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{triangle}}\:\mathrm{1},\boldsymbol{\mathrm{are}}\: \\ $$$$\boldsymbol{\mathrm{equail}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{length}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{medians}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{triangle}}\:\mathrm{2}. \\ $$$$\mathrm{1}.\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{ratio}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{areas}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{triangles}}. \\ $$$$\mathrm{2}.\boldsymbol{\mathrm{given}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{small}}\:\boldsymbol{\mathrm{side}}\:\boldsymbol{\mathrm{of}}\:\bigtriangleup_{\mathrm{1}} ,\:\boldsymbol{\mathrm{be}}\:\boldsymbol{\mathrm{equail}}\:\boldsymbol{\mathrm{to}}:\sqrt{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{one}}\:\boldsymbol{\mathrm{angle}}\:\boldsymbol{\mathrm{be}}:\mathrm{90}^{\bullet} . \\…
Question Number 2432 by prakash jain last updated on 19/Nov/15 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{3333}^{\mathrm{4444}} , \\ $$$$\mathrm{Say}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{3333}^{\mathrm{4444}} \:\mathrm{is}\:\mathrm{A}, \\ $$$$\mathrm{If}\:\mathrm{A}>\mathrm{10}\:\mathrm{then}\:\mathrm{sum}\:\mathrm{all}\:\mathrm{digits}\:\mathrm{of}\:\mathrm{A}. \\ $$$$\mathrm{This}\:\mathrm{process}\:\mathrm{is}\:\mathrm{repeated}\:\mathrm{until}\:\mathrm{a}\:\mathrm{single} \\ $$$$\mathrm{digits}\:\mathrm{sum}\:{x}\:\mathrm{in}\:\mathrm{obtained}. \\ $$$${x}=? \\ $$…
Question Number 133497 by Study last updated on 22/Feb/21 $${whaic}\:{is}\:{the}\:{large}\:{bracket} \\ $$$$\left\{\right\}\:?\:\:\:\:{or}\:\left[\right]\:? \\ $$ Commented by Rasheed.Sindhi last updated on 22/Feb/21 $$\left(\:\right)\:{is}\:{small}\:{brackets}. \\ $$$$\left\{\right\}\:{is}\:{middle}\:{brackets}. \\…
Question Number 67963 by mhmd last updated on 02/Sep/19 Commented by mathmax by abdo last updated on 02/Sep/19 $${generally}\:{if}\:{F}\left({x}\right)=\int_{{u}\left({x}\right)} ^{{v}\left({x}\right)} {f}\left({t}\right){dt}\:\Rightarrow{F}^{'} \left({x}\right)={v}^{'} \left({x}\right){f}\left({v}\left({x}\right)\right)−{u}^{'} \left({x}\right){f}\left({u}\left({x}\right)\right) \\…
Question Number 67960 by aseer imad last updated on 02/Sep/19 $$\frac{{d}}{{dx}}\left[{tan}^{−\mathrm{1}} \frac{\mathrm{4}{x}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}\right] \\ $$$${or} \\ $$$$\frac{{d}}{{dx}}{tan}^{−\mathrm{1}} \left(\mathrm{2}{tan}\theta\right)\:\:\:\:\:\:\:\left[{where}\:\mathrm{2}{x}={sin}\theta\:\right] \\ $$$$\:\:\:{which}\:{comes}\:{later}\:{if}\:{done}\:{considering} \\ $$$$\mathrm{2}{x}={sin}\theta \\ $$$${please}\:{help} \\…
Question Number 67958 by hmamarques1994@gmai.com last updated on 02/Sep/19 $$\: \\ $$$$\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{2}} {\boldsymbol{\mathrm{lim}}}\left(\frac{\mathrm{7}^{\sqrt[{\mathrm{3}}]{\boldsymbol{\mathrm{log}}_{\boldsymbol{\mathrm{x}}} \left(\mathrm{256}\right)}} −\mathrm{49}}{\mathrm{2}^{−\sqrt{\mathrm{2}^{\boldsymbol{\mathrm{x}}} }} −\frac{\mathrm{1}}{\mathrm{4}}}\right)\:\approx\:? \\ $$$$\: \\ $$ Terms of Service Privacy…
Question Number 67959 by mhmd last updated on 02/Sep/19 $$\int\sqrt{{e}^{{y}^{\mathrm{2}} } \:\:}\:{dy}\:\:{pleas}\:{sir}\:{can}\:{you}\:{help}\:{me}? \\ $$ Commented by Prithwish sen last updated on 02/Sep/19 $$\mathrm{please}\:\mathrm{check}\:\mathrm{Q67942}\:\mathrm{it}\:\mathrm{has}\:\mathrm{been}\:\mathrm{done} \\ $$…
Question Number 133494 by Eric002 last updated on 22/Feb/21 $${solve}\:{without}\:{using}\:{l}'{hopital}\:{and}\:{series}\: \\ $$$$\underset{{x}\rightarrow\mathrm{8}} {\mathrm{lim}}\frac{{x}\:\sqrt[{\mathrm{3}}]{{x}}−\mathrm{16}}{{x}−\mathrm{8}} \\ $$ Answered by Olaf last updated on 22/Feb/21 $$ \\ $$$$\mathrm{X}\:=\:\frac{{x}\sqrt[{\mathrm{3}}]{{x}}−\mathrm{16}}{{x}−\mathrm{8}}…