Question Number 7372 by FilupSmith last updated on 25/Aug/16 $$\boldsymbol{{v}}=\begin{bmatrix}{{x}}\\{{f}\left({x}\right)}\end{bmatrix},\:\:{f}\left({x}\right)={mx}+{b} \\ $$$$\mathrm{If}\:\mathrm{I}\:\mathrm{wish}\:\mathrm{to}\:\mathrm{rotate}\:\boldsymbol{{v}}\:\mathrm{counter}\:\mathrm{clockwise} \\ $$$$\mathrm{by}\:\theta\:\mathrm{degrees},\:\mathrm{how}\:\mathrm{does}\:\mathrm{one}\:\mathrm{do}\:\mathrm{so}\:\mathrm{where}: \\ $$$$\bullet\:\:\:\boldsymbol{{v}}\:\mathrm{is}\:\mathrm{rotated}\:\mathrm{about}\:\mathrm{the}\:\mathrm{origin} \\ $$$$\bullet\:\:\:\boldsymbol{{v}}\:\mathrm{is}\:\mathrm{rotated}\:\mathrm{about}\:\mathrm{the}\:\mathrm{point}\:\left({x}_{\mathrm{1}} ,\:{f}\left({x}_{\mathrm{1}} \right)\right) \\ $$$$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{new}\:\mathrm{vectors}? \\ $$ Answered…
Question Number 7369 by Tawakalitu. last updated on 25/Aug/16 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 72905 by Tony Lin last updated on 04/Nov/19 $${f}\left({x}\right)\geqslant\mathrm{0},\:{and}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{0},\underset{{x}\rightarrow{a}} {\mathrm{lim}}{g}\left({x}\right)=\infty \\ $$$${then}\:\underset{{x}\rightarrow{a}} {\mathrm{lim}}{f}\left({x}\right)^{{g}\left({x}\right)} =? \\ $$ Commented by mathmax by abdo last…
Question Number 138437 by EnterUsername last updated on 13/Apr/21 $$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2n}\right)!!}=\sqrt{\mathrm{e}} \\ $$ Answered by Ar Brandon last updated on 13/Apr/21 $$\:\:\:\:\:\left(\mathrm{2n}\right)!!=\mathrm{2n}\left(\mathrm{2n}−\mathrm{2}\right)\left(\mathrm{2n}−\mathrm{4}\right)…\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{2}^{\mathrm{n}}…
Question Number 72900 by aliesam last updated on 04/Nov/19 $${prove}\:{that}\: \\ $$$$ \\ $$$$−\mid{a}\mid\leqslant{a}\leqslant\mid{a}\mid \\ $$$$ \\ $$$${a}\:{is}\:{a}\:{real}\:{number} \\ $$ Answered by MJS last updated…
Question Number 7363 by Yozzia last updated on 25/Aug/16 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left\{\frac{\mathrm{1}}{{ln}\left({n}\right)}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\frac{{tan}^{−\mathrm{1}} {i}}{{n}+\mathrm{1}−{i}}\right)\right\}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7360 by rohit meena last updated on 24/Aug/16 Answered by Rasheed Soomro last updated on 25/Aug/16 $$\left(\mathrm{3}\right) \\ $$$$\:\:\:\:\:\:\:\left(\mathrm{4}−{k}\right){x}^{\mathrm{2}} +\mathrm{2}\left({k}+\mathrm{2}\right){x}+\mathrm{8}{k}+\mathrm{1} \\ $$$${The}\:{value}\:{of}\:\:{k},{for}\:{which}\:{the}\:{above} \\…
Question Number 72894 by TawaTawa last updated on 04/Nov/19 Answered by mind is power last updated on 04/Nov/19 $$\mathrm{lets}\:\mathrm{assum}\:\mathrm{n},\mathrm{m}\:\mathrm{are}\:\mathrm{relativ}\:\mathrm{prime} \\ $$$$ \\ $$$$\mathrm{let}\:\mathrm{N}=\mathrm{p}_{\mathrm{1}} ^{\mathrm{k1}} .\mathrm{p}_{\mathrm{2}}…
Question Number 138428 by tugu last updated on 13/Apr/21 $${what}\:{the}\:{area}\:{of}\:\:{area}\:{bounded}\:{by}\:{line} \\ $$$${y}=\:\mid{ln}\:{x}\mid\:{and}\:{y}=\:\mathrm{2}\: \\ $$ Answered by Ñï= last updated on 13/Apr/21 $$\mid{lnx}\mid=\mathrm{2} \\ $$$$\Rightarrow{x}={e}^{\mathrm{2}} ,{e}^{−\mathrm{2}}…
Question Number 138424 by tugu last updated on 13/Apr/21 $$\mid\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}} {\int}}\:\frac{{e}^{−{x}} {sin}\:{x}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx}\mid\leqslant\frac{\pi}{\mathrm{12}{e}} \\ $$ Commented by mitica last updated on 14/Apr/21 $$\exists{c}\in\left[\mathrm{1},\sqrt{\mathrm{3}}\right],\underset{\mathrm{1}} {\overset{\sqrt{\mathrm{3}}}…