Question Number 66171 by mathmax by abdo last updated on 10/Aug/19 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left\{{sin}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)+\mathrm{2}{sin}\left(\frac{\mathrm{4}}{{n}^{\mathrm{2}} }\right)+….\left({n}−\mathrm{1}\right){sin}\left(\frac{\left({n}−\mathrm{1}\right)^{\mathrm{2}} }{{n}^{\mathrm{2}} }\right)\right\} \\ $$ Commented by mathmax by abdo…
Question Number 66168 by mathmax by abdo last updated on 10/Aug/19 $${prove}\:{without}\:{calculus}\:{that}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}=\int_{\mathrm{0}} ^{\infty} {sin}\left({x}^{\mathrm{2}} \right){dx} \\ $$ Terms of Service Privacy Policy…
Question Number 131706 by bounhome last updated on 07/Feb/21 $$\int{e}^{\mathrm{3}{x}} {cosxdx}=\:?\:{help}\:{me}\:{please}\: \\ $$ Answered by mathmax by abdo last updated on 07/Feb/21 $$\int\:\mathrm{e}^{\mathrm{3x}} \:\mathrm{cosx}\:\mathrm{dx}\:=\mathrm{Re}\left(\int\:\mathrm{e}^{\mathrm{3x}} \:\mathrm{e}^{\mathrm{ix}}…
Question Number 66169 by mathmax by abdo last updated on 10/Aug/19 $${find}\:{the}\:{values}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:{cos}\left({x}^{\mathrm{2}} \right){dx}\:{and}\:\int_{\mathrm{0}} ^{\infty} \:{sin}\left({x}^{\mathrm{2}} \right){dx}\left({fresnel}\:{integrals}\right) \\ $$$${by}\:{using}\:\Gamma\left({z}\right)\:=\int_{\mathrm{0}} ^{\infty} \:{t}^{{z}−\mathrm{1}} \:{e}^{−{t}} \:{dt}\:\: \\…
Question Number 630 by 123456 last updated on 15/Feb/15 $$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{+\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}{dx} \\ $$$$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{+\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\mathrm{cos}\left(\mathrm{2}{nx}\right){dx} \\ $$$$\underset{−\frac{\pi}{\mathrm{2}}} {\overset{+\frac{\pi}{\mathrm{2}}} {\int}}\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\mathrm{sin}\left(\mathrm{2}{nx}\right){dx} \\ $$$${n}\in\mathbb{N}^{\ast} \\ $$ Commented…
Question Number 628 by malwaan last updated on 14/Feb/15 $$\int_{\frac{\mathrm{3}}{\mathrm{2}}} ^{\mathrm{2}} \left(\frac{{x}−\mathrm{1}}{\mathrm{3}−{x}}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} {dx} \\ $$ Commented by malwaan1 last updated on 26/Feb/15 $${what}\:{about}\:{the}\:{indefinie}\:{integral}\:? \\ $$…
Question Number 131697 by mathlove last updated on 07/Feb/21 $${x}^{{x}} =\mathrm{6}\:\:\:\:\:\:\:\:\:\:{x}=? \\ $$ Answered by mr W last updated on 07/Feb/21 $${x}=\mathrm{6}^{\frac{\mathrm{1}}{{x}}} ={e}^{\frac{\mathrm{ln}\:\mathrm{6}}{{x}}} \\ $$$$\frac{\mathrm{1}}{{x}}{e}^{\frac{\mathrm{ln}\:\mathrm{6}}{{x}}}…
Question Number 66162 by peter frank last updated on 09/Aug/19 Commented by mr W last updated on 10/Aug/19 $${question}\:{is}\:{not}\:{clear}.\:{have}\:{you}\:{got} \\ $$$${a}\:{diagram}? \\ $$ Commented by…
Question Number 66163 by aliesam last updated on 09/Aug/19 Answered by mr W last updated on 09/Aug/19 $${y}={x}^{{x}^{{x}^{….} } } \\ $$$${y}={x}^{{y}} \\ $$$$\mathrm{ln}\:{y}={y}\:\mathrm{ln}\:{x} \\…
Question Number 66160 by Tanmay chaudhury last updated on 09/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com