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lim-t-0-pi-sin-tx-x-dx-

Question Number 207801 by naka3546 last updated on 27/May/24 $$\underset{{t}\rightarrow\infty} {\mathrm{lim}}\:\:\underset{\mathrm{0}} {\overset{\:\:\:\:\:\:\pi} {\int}}\:\:\frac{\mathrm{sin}\:\left(\mathrm{t}{x}\right)}{{x}}\:{dx}\:\:=\:\centerdot\centerdot\centerdot \\ $$ Commented by naka3546 last updated on 27/May/24 $${t}\:\rightarrow\infty \\ $$…

prove-that-vector-scalar-vector-

Question Number 207812 by Davidtim last updated on 27/May/24 $${prove}\:{that}\:\frac{{vector}}{{scalar}}={vector} \\ $$ Answered by A5T last updated on 27/May/24 $${Let}\:{scalar}=\lambda\in\mathbb{R};\:{and}\:{vector},\boldsymbol{{a}}=\left({a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ,…,{a}_{{n}} \right)\in\mathbb{R}_{{n}} \\ $$$${where}\:{each}\:{a}_{{i}}…

lim-0-1-e-ncos-x-dx-

Question Number 207723 by SANOGO last updated on 24/May/24 $$\mathrm{li}{m}\int_{\mathrm{0}} ^{\infty} \left(\mathrm{1}−{e}^{−{ncos}\left({x}\right)} \right){dx} \\ $$ Commented by Frix last updated on 24/May/24 $${f}\left({x}\right)=\mathrm{1}−\mathrm{e}^{−{n}\mathrm{cos}\:{x}} \\ $$$${n}\rightarrow\infty\:\Rightarrow\:{f}\left({x}\right)=\begin{cases}{\mathrm{1};\:−\frac{\pi}{\mathrm{2}}+{k}\pi\leqslant{x}\leqslant\frac{\pi}{\mathrm{2}}+{k}\pi}\\{−\infty;\:\frac{\pi}{\mathrm{2}}+{k}\pi<{x}<\frac{\mathrm{3}\pi}{\mathrm{2}}+{k}\pi}\end{cases}\forall{k}\in\mathbb{Z}…