Question Number 127042 by benjo_mathlover last updated on 26/Dec/20 $$\:\int_{\mathrm{1}/\sqrt{\mathrm{2}}} ^{\:\mathrm{1}} \frac{\mathrm{arcsin}\:{x}}{{x}^{\mathrm{3}} }\:{dx}\:? \\ $$$$\:'\:{not}\:{nice}\:{integral}\:'\: \\ $$ Commented by liberty last updated on 26/Dec/20 ��������…
Question Number 192573 by senestro last updated on 21/May/23 $${solve}; \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}^{\mathrm{2}} {tan}\left(\frac{{sin}\pi{x}}{\mathrm{2}{x}}\right) \\ $$$${solution} \\ $$$${let}\:{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}{x}^{\mathrm{2}} {tan}\left(\frac{{sin}\pi{x}}{\mathrm{2}{x}}\right) \\ $$$${since}\:{sinx}\sim{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}\: \\ $$$${L}=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 192572 by naka3546 last updated on 21/May/23 $$\mathrm{Let}\:\:{ABCD}\:\:\mathrm{be}\:\:\mathrm{a}\:\:\mathrm{rectangle}\:\:\mathrm{having}\:\:\mathrm{an}\:\mathrm{area}\:\:\mathrm{of}\:\:\mathrm{290}. \\ $$$$\mathrm{Let}\:\:{E}\:\:\mathrm{be}\:\:\mathrm{on}\:\:{BC}\:\:\mathrm{such}\:\:\mathrm{that}\:\:{BE}\::\:{BC}\:=\:\mathrm{3}\::\:\mathrm{2}. \\ $$$$\mathrm{Let}\:\:{F}\:\:\mathrm{be}\:\:\mathrm{on}\:\:{CD}\:\:\mathrm{such}\:\:\mathrm{that}\:\:{CF}\::\:{FD}\:=\:\mathrm{3}\::\:\mathrm{1}. \\ $$$$\mathrm{If}\:\:{G}\:\:\mathrm{is}\:\:\mathrm{the}\:\:\mathrm{intersection}\:\:\mathrm{of}\:\:{AE}\:\:\mathrm{and}\:\:{BF},\:\:\mathrm{compute} \\ $$$$\mathrm{the}\:\:\mathrm{area}\:\:\mathrm{of}\:\:\bigtriangleup{BEG}. \\ $$ Terms of Service Privacy Policy…
Question Number 127032 by mnjuly1970 last updated on 26/Dec/20 Answered by Olaf last updated on 26/Dec/20 $$\left.{i}\right) \\ $$$$\mathrm{1}−\mathrm{2}{r}\mathrm{cos}{x}+{r}^{\mathrm{2}} \:=\:\left({e}^{{ix}} −{r}\right)\left({e}^{−{ix}} −{r}\right) \\ $$$$\mathrm{R}_{{x}} \left({r}\right)\:=\:\frac{\mathrm{1}−{r}^{\mathrm{2}}…
Question Number 192570 by mechanics last updated on 21/May/23 Answered by cortano12 last updated on 21/May/23 $$\:\mid\mathrm{x}^{\mathrm{2}} −\mathrm{4}\mid<\mathrm{5} \\ $$$$\:\left(\mathrm{x}^{\mathrm{2}} −\mathrm{9}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)<\mathrm{0} \\ $$$$\:\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)<\mathrm{0}…
Question Number 61495 by bhanukumarb2@gmail.com last updated on 03/Jun/19 Commented by bhanukumarb2@gmail.com last updated on 03/Jun/19 $${prove}\:{second}\:{in}\:{which}\:{book}\:{i}\:{can}\:{get}\: \\ $$$${these}\:{type}\:{approximation} \\ $$ Commented by bhanukumarb2@gmail.com last…
Question Number 192560 by Ari last updated on 20/May/23 Commented by dubylee last updated on 22/May/23 $${what}\:{is}\:{the}\:{question}\:{here}? \\ $$ Commented by Skabetix last updated on…
Question Number 61490 by MJS last updated on 03/Jun/19 $$\sqrt{{a}−\sqrt{{a}+{x}}}+\sqrt{{a}+\sqrt{{a}−{x}}}=\mathrm{2}{x} \\ $$$$\mathrm{this}\:\mathrm{is}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{Sir}\:\mathrm{Aifour}\:\mathrm{and}\:\mathrm{me}\:\mathrm{found} \\ $$$$ \\ $$$$\mathrm{trivial}\:\mathrm{solution}\:{a}={x}=\mathrm{0} \\ $$$$ \\ $$$${a},\:{x}\:\in\mathbb{R} \\ $$$$ \\ $$$${x}=\frac{\sqrt{\mathrm{2}}}{\mathrm{8}}\left({r}+\sqrt{{r}^{\mathrm{2}} +\mathrm{4}}\right)\sqrt{\mathrm{2}\left(\mathrm{4}{a}−\mathrm{1}\right)−{r}^{\mathrm{2}}…
Question Number 127020 by bramlexs22 last updated on 26/Dec/20 $$\:\:{super}\:{nice}\:! \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{show}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\zeta\left(\mathrm{6}\right)\:=\:\frac{\pi^{\mathrm{6}} }{\mathrm{945}} \\ $$ Commented by liberty last updated on 26/Dec/20 $${hahaha}\:{very}\:{nice}\:…
Question Number 127018 by ‘-E/9 last updated on 26/Dec/20 $${Vf}×\mathrm{2}={Vi}×\mathrm{2}+\mathrm{2}{a}\Delta{d} \\ $$$$\mathrm{0}=\mathrm{16}.\mathrm{5} \\ $$ Answered by physicstutes last updated on 26/Dec/20 $$\mathrm{you}\:\mathrm{should}\:\mathrm{write}\:\mathrm{it}\:\mathrm{this}\:\mathrm{way}. \\ $$$$\:\:{v}_{{f}} ^{\mathrm{2}}…