Question Number 9237 by geovane10math last updated on 25/Nov/16 $${About}\:{the}\:{Euler}-{Mascheroni}\:{constant} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\gamma\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:−\:\mathrm{ln}\:{n}\right) \\ $$$${Why}\:{the}\:{limit}\:{converges}\:{if} \\ $$$$\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:−\:\mathrm{ln}\:{n}\right)\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}}\:−\:\underset{{n}\rightarrow\infty}…
Question Number 140310 by liberty last updated on 06/May/21 $$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{dx}\:=\:\mathrm{0} \\ $$ Answered by qaz last updated on 06/May/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 9236 by tawakalitu last updated on 24/Nov/16 $$\mathrm{Solve}\:\:\mathrm{simultaneously} \\ $$$$\frac{\mathrm{x}}{\mathrm{y}\:+\:\mathrm{1}_{\:} }\:+\:\frac{\mathrm{y}}{\mathrm{x}\:+\:\mathrm{1}}\:=\:\frac{\mathrm{5}}{\mathrm{3}}\:\:\:\:………….\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{2}\:\:\:\:\:\:\:\:………..\:\left(\mathrm{ii}\right) \\ $$ Answered by RasheedSoomro last updated on…
Question Number 9233 by geovane10math last updated on 24/Nov/16 $$\mathrm{The}\:\mathrm{gamma}\:\mathrm{function}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Gamma\left({s}\right)\:=\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}} {x}^{{s}−\mathrm{1}} \:{dx} \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{gamma}\:\mathrm{function} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{and}\:\mathrm{not}\:\mathrm{time}-\mathrm{consuming}\: \\ $$$$\mathrm{way}? \\ $$$$ \\…
Question Number 9232 by geovane10math last updated on 24/Nov/16 $$\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:\mathrm{4}\:+…+\:{n}\:=\:\frac{{n}\left({n}\:+\:\mathrm{1}\right)}{\mathrm{2}} \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} \:+\mathrm{3}^{\mathrm{2}} \:+…+\:{n}^{\mathrm{2}} \:=\:\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$$$\mathrm{1}^{{x}} \:+\:\mathrm{2}^{{x}} \:+\:\mathrm{3}^{{x}} \:+…+\:=\:{n}^{{x}} \:=\:\mathrm{Formula}? \\ $$$${x}\:\in\:\mathbb{R} \\…
Question Number 74766 by chess1 last updated on 30/Nov/19 Commented by mathmax by abdo last updated on 30/Nov/19 $${changement}\:\frac{\mathrm{1}}{{x}}={t}\:{lead}\:{yo}\:{lim}_{{t}\rightarrow+\infty} \sqrt{{t}+\sqrt{{t}+\sqrt{{t}}}}\:−\sqrt{{t}−\sqrt{{t}+\sqrt{{t}}}} \\ $$$$={lim}_{{t}\rightarrow+\infty} {g}\left({t}\right)\:\:{we}\:{have}\:\:\sqrt{{t}+\sqrt{{t}}}=\sqrt{{t}}×\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{{t}}}}\sim\sqrt{{t}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}\sqrt{{t}}}\right) \\ $$$$=\sqrt{{t}}+\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\sqrt{{t}+\sqrt{{t}+\sqrt{{t}}}}\sim\sqrt{{t}+\sqrt{{t}}+\frac{\mathrm{1}}{\mathrm{2}}}\:{also}\:\sqrt{{t}−\sqrt{{t}+\sqrt{{t}}}}\sim\sqrt{{t}−\sqrt{{t}}−\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 9231 by tawakalitu last updated on 24/Nov/16 $$\mathrm{Differentiate}\::\:\:\mathrm{sin}\sqrt{\mathrm{x}}\:\:\:\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{first}\:\mathrm{principle}. \\ $$ Answered by mrW last updated on 29/Nov/16 $$\mathrm{y}\left(\mathrm{x}\right)=\mathrm{sin}\:\sqrt{\mathrm{x}} \\ $$$$\mathrm{y}\left(\mathrm{x}+\mathrm{h}\right)=\mathrm{sin}\:\sqrt{\mathrm{x}+\mathrm{h}} \\…
Question Number 9230 by tawakalitu last updated on 24/Nov/16 $$\mathrm{Given}\:\mathrm{that}\: \\ $$$$\mathrm{a}\:=\:\mathrm{2i}\:−\:\mathrm{3j}\:+\:\mathrm{k},\:\mathrm{b}\:=\:\mathrm{4i}\:+\:\mathrm{j}\:−\:\mathrm{3k}, \\ $$$$\mathrm{c}\:=\:\mathrm{i}\:−\:\mathrm{3k} \\ $$$$\mathrm{Find}\:\:\left(\mathrm{a}\centerdot\mathrm{b}\right)\mathrm{c},\:\:\mathrm{a}\left(\mathrm{b}×\mathrm{c}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 9229 by tawakalitu last updated on 24/Nov/16 $$\mathrm{2}^{\mathrm{3x}\:+\:\mathrm{1}} \:−\:\mathrm{3}.\mathrm{2}^{\mathrm{2x}} \:+\:\mathrm{2}^{\mathrm{x}\:+\:\mathrm{1}} \:=\:\mathrm{2x} \\ $$$$\mathrm{Find}\:\mathrm{x} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140296 by Satyendra last updated on 06/May/21 $$\int_{\mathrm{2}} ^{\mathrm{5}} \frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }} \\ $$ Answered by Dwaipayan Shikari last updated on 06/May/21 $$\int\frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{4}} }}…