Question Number 135820 by Ar Brandon last updated on 16/Mar/21 $$\mathrm{Let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} {e}^{−{t}^{\mathrm{2}} } {dt}\:, \\ $$$$\mathrm{Prove}\:\int_{\mathrm{0}} ^{\infty} {e}^{−{x}^{\mathrm{2}} +{f}\left({x}\right)} {dx}={e}^{\frac{\sqrt{\pi}}{\mathrm{2}}} −\mathrm{1}. \\ $$ Answered…
Question Number 70287 by MJS last updated on 02/Oct/19 $$\mathrm{I}\:\mathrm{wanted}\:\mathrm{to}\:\mathrm{say}\:\mathrm{this}\:\mathrm{earlier}… \\ $$$$\mathrm{I}\:\mathrm{love}\:\mathrm{mathematics}\:\mathrm{and}\:\mathrm{I}\:\mathrm{also}\:\mathrm{love}\:\mathrm{people}. \\ $$$$\mathrm{But}\:\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{here}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{same}\:\mathrm{old}\:\mathrm{boring} \\ $$$$\mathrm{problems}\:\mathrm{copied}\:\mathrm{from}\:\mathrm{facebook}\:\mathrm{or}\:\mathrm{whatsapp} \\ $$$$\mathrm{or}\:\mathrm{other}\:\mathrm{platforms}.\:\mathrm{They}\:\mathrm{are}\:\mathrm{not}\:\mathrm{interesting} \\ $$$$\mathrm{at}\:\mathrm{all}.\:\mathrm{They}\:\mathrm{have}\:\mathrm{been}\:\mathrm{coming}\:\mathrm{in}\:\mathrm{as}\:\mathrm{a}\:\mathrm{kind} \\ $$$$\mathrm{of}\:\mathrm{competition},\:\mathrm{or}\:\mathrm{simply}\:\mathrm{to}\:\mathrm{brag},\:\mathrm{they}'\mathrm{ve} \\ $$$$\mathrm{been}\:\mathrm{traded}\:\mathrm{from}\:\mathrm{one}\:\mathrm{non}−\mathrm{mathematician} \\…
Question Number 4750 by 123456 last updated on 04/Mar/16 $${f}_{{n}} \left({x}\right)=\begin{cases}{\mathrm{1}\:\:\:\:{n}=\mathrm{1}}\\{\frac{\left(\mathrm{1}−{x}^{\mathrm{2}} \right)…\left(\mathrm{1}−{x}^{{n}} \right)}{\left(\mathrm{1}−\mathrm{2}{x}\right)…\left(\mathrm{1}−{nx}\right)}\:\:\:\:{n}\in\mathbb{N},{n}>\mathrm{1}}\end{cases} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}{f}_{{n}} \left({x}\right)=? \\ $$$${n}>\mathrm{1},{f}\left({x}\right)=\mathrm{0},{x}=? \\ $$ Commented by prakash jain…
Question Number 135823 by Khakie last updated on 16/Mar/21 $${how}\:{can}\:{this}\:{be}\:{equal}??? \\ $$$${sin}\:{wt}\:\:=\:{e}^{−{at}} \: \\ $$$$ \\ $$ Commented by mr W last updated on 16/Mar/21…
Question Number 135822 by Khakie last updated on 16/Mar/21 $$\left[\frac{{sin}\alpha}{\alpha}\right]^{\mathrm{2}} \:=\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:{please}\:{solve}\:{this} \\ $$ Commented by mr W last updated on 16/Mar/21 $${no}\:{exact}\:{solution}\:{possible}. \\ $$$$\alpha\approx\mathrm{1}.\mathrm{3916} \\…
Question Number 4748 by Yozzii last updated on 04/Mar/16 $${Find}\:{all}\:{real}\:\boldsymbol{{a}}\:{such}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{f}\left({x}\right)=\left\{\boldsymbol{{a}}{x}+{sinx}\right\}\: \\ $$$${is}\:{periodic}.\:\left\{{u}\right\}\:{is}\:{the}\:{fractional}−{part} \\ $$$${function}\:{of}\:{the}\:{real}\:{number}\:{u}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135816 by ShiimiGee last updated on 16/Mar/21 Commented by ShiimiGee last updated on 16/Mar/21 $$ \\ $$ Commented by liberty last updated on…
Question Number 135818 by mr W last updated on 16/Mar/21 Commented by mr W last updated on 16/Mar/21 $${unsolved}\:{old}\:{question} \\ $$$${see}\:{Q}\mathrm{74557} \\ $$ Answered by…
Question Number 70277 by mr W last updated on 02/Oct/19 Answered by mind is power last updated on 02/Oct/19 $$\frac{{a}}{{sin}\left(\theta\right)}=\frac{\mathrm{2}{a}}{{Sin}\left(\pi−\mathrm{3}\theta\right)}=\frac{\mathrm{2}{a}}{{sin}\left(\mathrm{3}\theta\right)} \\ $$$$\Rightarrow{sin}\left(\mathrm{3}\theta\right)=\mathrm{2}{sin}\left(\theta\right) \\ $$$${sin}\left(\mathrm{3}\theta\right)=−\mathrm{4}{sin}^{\mathrm{3}} \left(\theta\right)+\mathrm{3}{sin}\left(\theta\right)…
Question Number 4739 by shashi kashyap last updated on 04/Mar/16 Answered by 123456 last updated on 04/Mar/16 $${x}^{\mathrm{2}} −{xy}^{\mathrm{2}} +\mathrm{3}{y}^{\mathrm{2}} +\mathrm{2}=\mathrm{0} \\ $$$$\left(\mathrm{3}−{x}\right){y}^{\mathrm{2}} =−{x}^{\mathrm{2}} −\mathrm{2}…