Question Number 219659 by Nicholas666 last updated on 30/Apr/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}; \\ $$$$\:\:{cos}\:\left({B}+{C}−{A}\right)−{cos}\left({C}+{A}−{B}\right)+{cos}\left({A}+{B}−{C}\right)−{cos}\left({A}+{B}+{C}\right)\:=\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}{sinAcosBsinC} \\ $$$$ \\ $$ Answered by som(math1967) last updated…
Question Number 219685 by alcohol last updated on 30/Apr/25 Answered by SdC355 last updated on 01/May/25 $$\kappa=\frac{\mathrm{2}}{\:\sqrt{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}} \right)^{\mathrm{3}} }}\:\:\:\left(\mathrm{curvature}\:\kappa=\frac{\mid\mid{y}^{\left(\mathrm{2}\right)} \left({t}\right)\mid\mid}{\:\sqrt{\left(\mathrm{1}+\left({y}^{\left(\mathrm{1}\right)} \left({t}\right)\right)^{\mathrm{2}} \right)^{\mathrm{3}} }}\:\right) \\ $$$${r}=\frac{\mathrm{1}}{\kappa}=\frac{\sqrt{\left(\mathrm{1}+\mathrm{4}{x}^{\mathrm{2}}…
Question Number 219649 by SdC355 last updated on 30/Apr/25 $$\mathrm{Solve}\:{y}^{\left(\mathrm{2}\right)} \left({t}\right)−{t}\centerdot{y}\left({t}\right)=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219682 by Nicholas666 last updated on 30/Apr/25 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{log}\left(\mathrm{1}+{x}\right)\centerdot\mathrm{Li}_{{s}} \left({x}\right)}{{x}\centerdot\zeta\left({s}+\mathrm{1},{x}\right)}\:{dx} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 219651 by SdC355 last updated on 30/Apr/25 $$\mathrm{Solve} \\ $$$${x}^{\mathrm{2}} {y}^{\left(\mathrm{2}\right)} \left({x}\right)+{xy}^{\left(\mathrm{1}\right)} \left({x}\right)+\left({x}^{\mathrm{2}} −\nu^{\mathrm{2}} \right){y}\left({x}\right)={e}^{−{kx}} \\ $$ Answered by MrGaster last updated on…
Question Number 219580 by SdC355 last updated on 29/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \:{J}_{\nu} \left({kt}\right){e}^{−{t}} \:\mathrm{d}{t} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219581 by nothing48 last updated on 29/Apr/25 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 219577 by SdC355 last updated on 29/Apr/25 $$\mathrm{prove} \\ $$$$\underset{{n}\:\mathrm{times}} {\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} …\int_{\mathrm{0}} ^{\:\mathrm{1}} }\:\:{x}_{\mathrm{1}} ^{\alpha} {x}_{\mathrm{2}} ^{\alpha} ….{x}_{{n}} ^{\alpha} \mathrm{ln}\left({x}_{\mathrm{1}}…
Question Number 219579 by SdC355 last updated on 29/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \:\:\mathrm{sin}\left({t}\right){J}_{\nu} \left({kt}\right)\:\mathrm{d}{t} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\:{t}\centerdot{J}_{\nu} \left({at}\right){J}_{\nu} \left({kt}\right)\:\mathrm{d}{t} \\ $$ Terms of Service Privacy…
Question Number 219574 by SdC355 last updated on 29/Apr/25 $$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{sin}\left({z}\right)}{{z}\left({z}^{\mathrm{2}} +\mathrm{4}\right)}\:\mathrm{d}{z}=\frac{\mathrm{1}}{\mathrm{4}}\int_{\mathrm{0}} ^{\:\infty} \:\:\left(\frac{\mathrm{sin}\left({z}\right)}{{z}}−\frac{\mathrm{sin}\left({z}\right)}{\mathrm{2}{z}+\mathrm{4}\boldsymbol{{i}}}−\frac{\mathrm{sin}\left({z}\right)}{\mathrm{2}{z}−\mathrm{4}\boldsymbol{{i}}}\right)\:\mathrm{d}{z} \\ $$$$\mathrm{and}\:\mathrm{next}….??? \\ $$$$\mathrm{2}\pi\boldsymbol{{i}}\underset{{j}=\mathrm{1}} {\overset{{M}} {\sum}}\:\:\mathrm{Res}_{{h}={a}_{{j}} } \left\{{f}\left({h}\right)\right\}…. \\ $$…