Question Number 75083 by Rio Michael last updated on 07/Dec/19 $${A}\:{function}\:{f}\:{is}\:{given}\:{by}\: \\ $$$$\:{f}\left({x}\right)\:=\:\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3},\:\:\mathrm{0}\leqslant{x}<\mathrm{2}}\\{\mathrm{4}{x}−\mathrm{7},\:\mathrm{2}\leqslant{x}<\mathrm{4}}\end{cases} \\ $$$${is}\:{such}\:{that}\:{f}\left({x}\right)\:=\:{f}\left({x}\:+\:\mathrm{4}\right)\: \\ $$$${find}\:\:{f}\left(\mathrm{27}\right)\:{and}\:{f}\left(−\mathrm{106}\right). \\ $$ Answered by MJS last updated…
Question Number 75080 by ~blr237~ last updated on 07/Dec/19 $$\mathrm{Find}\:\mathrm{out}\: \\ $$$$\mathrm{A}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \left(\mathrm{1}−\sqrt{\mathrm{sinx}}\right)^{\mathrm{n}} \mathrm{cosxdx} \\ $$ Commented by mathmax by abdo last…
Question Number 75081 by Rio Michael last updated on 07/Dec/19 $${Evaluate}\: \\ $$$$\:\int_{\mathrm{1}} ^{\mathrm{3}\:} \frac{{x}^{\mathrm{2}} }{\mathrm{1}+{x}}\:{dx} \\ $$ Answered by mr W last updated on…
Question Number 9544 by tawakalitu last updated on 14/Dec/16 Answered by ridwan balatif last updated on 15/Dec/16 $$\mathrm{r}_{\mathrm{1}} =+\mathrm{22}.\mathrm{4cm}\:\mathrm{and}\:\mathrm{r}_{\mathrm{2}} =+\mathrm{46}.\mathrm{2}\:\mathrm{cm} \\ $$$$\frac{\mathrm{1}}{\mathrm{f}}=\left(\mathrm{n}−\mathrm{1}\right)\left(\frac{\mathrm{1}}{\mathrm{r}_{\mathrm{1}} }−\frac{\mathrm{1}}{\mathrm{r}_{\mathrm{2}} }\right) \\…
Question Number 75078 by ~blr237~ last updated on 07/Dec/19 Answered by MJS last updated on 07/Dec/19 $$\mathrm{the}\:\mathrm{diagonal}\:\mathrm{is} \\ $$$$\sqrt{\left(\mathrm{14}+\mathrm{9}\right)^{\mathrm{2}} +\mathrm{7}^{\mathrm{2}} }=\mathrm{17}\sqrt{\mathrm{2}} \\ $$$$\Rightarrow\:{x}=\mathrm{17} \\ $$…
Question Number 9543 by Joel575 last updated on 14/Dec/16 $$\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{x}} \:+\:\left(\mathrm{7}−\mathrm{4}\sqrt{\mathrm{3}}\right)\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{x}} \:=\:\mathrm{4}\left(\mathrm{2}−\sqrt{\mathrm{3}}\right),\:{x}\:\neq\:\mathrm{0} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:?\: \\ $$ Answered by mrW last updated on 14/Dec/16 $$\mathrm{u}=\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{x}} \\…
Question Number 75079 by ~blr237~ last updated on 07/Dec/19 $$\mathrm{Let}\:\mathrm{f}\in\mathrm{C}\left(\left[\mathrm{0},\mathrm{1}\right],\left[\mathrm{0},\mathrm{1}\right]\right)\:\: \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\:\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{n}} } \mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{x}_{\mathrm{i}} \:\right)\mathrm{dx}_{\mathrm{1}} ….\mathrm{dx}_{\mathrm{n}} \:=\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$ Terms of Service…
Question Number 140615 by bramlexs22 last updated on 10/May/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{common}\: \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{12x}\:\mathrm{and} \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\:\mathrm{24x}\:. \\ $$ Answered by EDWIN88 last updated on…
Question Number 9541 by FilupSmith last updated on 14/Dec/16 $$\int\left(−\mathrm{1}\right)^{{x}} {xdx}=?? \\ $$ Answered by FilupSmith last updated on 15/Dec/16 $$\int\left(−\mathrm{1}\right)^{{x}} {xdx}=\int{e}^{{x}\mathrm{ln}\left(−\mathrm{1}\right)} {xdx} \\ $$$$=\int{e}^{{xi}\pi}…
Question Number 140614 by bramlexs22 last updated on 10/May/21 $$\int\:_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{ln}\:\left(\mathrm{sin}\:\mathrm{x}\right)\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{dx}\:=?\: \\ $$$$ \\ $$ Answered by bemath last updated on 10/May/21 Answered…