Question Number 892 by Karting7442 last updated on 14/Apr/15 $$\frac{−\mathrm{5}+{x}}{\mathrm{22}}=−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:{check} \\ $$$$\:\: \\ $$$$\:\:\:{what}\:{is}\:{x}?{also}\:{check}\:{it}. \\ $$ Answered by prakash jain last updated on 14/Apr/15 $$\frac{−\mathrm{5}+{x}}{\mathrm{22}}×\mathrm{22}=−\mathrm{1}×\mathrm{22}…
Question Number 131961 by Zack_ last updated on 10/Feb/21 $$\int\left({sin}^{\mathrm{4}} {x}.{cos}^{\mathrm{4}} {x}\right){dx} \\ $$ Answered by liberty last updated on 10/Feb/21 $$\mathrm{I}=\int\:\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}\right)^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{2x}\right)^{\mathrm{2}} \mathrm{dx} \\…
Question Number 891 by 123456 last updated on 17/Apr/15 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{lets}\:{e}_{{n}} :\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{lets}\:{a}_{{n}} :\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}\right)=\underset{{i}=\mathrm{1}} {\overset{\mathrm{3}} {\sum}}{a}_{{i}} \left({x}\right){e}_{{i}} \left({x}\right) \\…
Question Number 131960 by liberty last updated on 10/Feb/21 Answered by mr W last updated on 10/Feb/21 $${r}^{\mathrm{2}} +{h}^{\mathrm{2}} =\left(\sqrt{\mathrm{3}}\right)^{\mathrm{2}} \:\Rightarrow{r}^{\mathrm{2}} =\mathrm{3}−{h}^{\mathrm{2}} \\ $$$${V}=\frac{\pi}{\mathrm{3}}{r}^{\mathrm{2}} {h}=\frac{\pi}{\mathrm{3}}\left(\mathrm{3}−{h}^{\mathrm{2}}…
Question Number 131962 by EDWIN88 last updated on 10/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}\:−\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)=? \\ $$ Answered by liberty last updated on 10/Feb/21 $$\:\mathrm{let}\:\mathrm{u}=\mathrm{ln}\:\mathrm{x}\:\Rightarrow\mathrm{x}=\mathrm{e}^{\mathrm{u}} \\ $$$$\:\underset{\mathrm{u}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{u}}−\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{u}}…
Question Number 888 by Karting7442 last updated on 14/Apr/15 $$\frac{{x}+\mathrm{9}}{\mathrm{2}}=\mathrm{3} \\ $$$${what}\:{is}\:{x}? \\ $$ Answered by 123456 last updated on 14/Apr/15 $$\frac{{x}+\mathrm{9}}{\mathrm{2}}=\mathrm{3} \\ $$$$\frac{{x}+\mathrm{9}}{\mathrm{2}}×\mathrm{2}=\mathrm{3}×\mathrm{2} \\…
Question Number 131957 by rs4089 last updated on 10/Feb/21 $${Evaluate}\:\:\int_{−\infty} ^{\infty} \frac{{sinx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 10/Feb/21 $$\int_{−\infty} ^{\infty}…
Question Number 887 by Karting7442 last updated on 14/Apr/15 $$ \\ $$$$ \\ $$$$\:\:\:\:\frac{−\mathrm{5}+{x}}{\mathrm{22}}=\mathrm{1} \\ $$$${what}\:{is}\:{x}? \\ $$ Answered by 123456 last updated on 14/Apr/15…
Question Number 66420 by Rio Michael last updated on 14/Aug/19 $${solve}\:{the}\:{differential}\:{equation} \\ $$$$\:\mathrm{2}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\frac{{dy}}{{dx}}\:−\:{e}^{−{x}} \:=\:\mathrm{4} \\ $$ Commented by mathmax by abdo last updated…
Question Number 66421 by Rio Michael last updated on 14/Aug/19 $${show}\:{that}\:{for}\:{a}\:{given}\:{complex}\:{number}\:{z} \\ $$$$\:{z}^{{n}} \:=\:{r}^{{n}} \:\left({cosn}\theta\:+\:{isinn}\theta\right)\: \\ $$ Answered by MJS last updated on 14/Aug/19 $${z}={r}\left(\mathrm{cos}\:\theta\:+\mathrm{i}\:\mathrm{sin}\:\theta\right)={r}\mathrm{e}^{\mathrm{i}\theta}…