Question Number 136437 by liberty last updated on 22/Mar/21 $${Find}\:{max}\:{and}\:{min}\:{value}\:{of}\: \\ $$$${y}\:=\:\mathrm{sin}\:^{\mathrm{2}} {x}+\:\mathrm{cos}\:^{\mathrm{4}} {x}\: \\ $$ Answered by rs4089 last updated on 22/Mar/21 $${y}=\mathrm{1}−{cos}^{\mathrm{2}} {x}+{cos}^{\mathrm{4}}…
Question Number 5365 by sanusihammed last updated on 11/May/16 $${If}\:\:{y}\:=\:{x}^{{x}^{{x}^{{x}} } } \:\:\:.\:\:{Find}\:{dy}/{dx} \\ $$ Answered by Yozzii last updated on 11/May/16 $${lny}={x}^{{x}^{{x}} } {lnx}\:\:\:\left({x}>\mathrm{0}\right)…
Question Number 5364 by sanusihammed last updated on 11/May/16 $${Find}\:{the}\:{integral}\:{solution}\:{of}\:\:\:\:\:\:{x}^{{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136433 by metamorfose last updated on 21/Mar/21 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{C}_{\mathrm{2}{n}+\mathrm{1}} ^{\mathrm{2}{k}+\mathrm{1}} \mathrm{8}^{{k}} =…??? \\ $$ Answered by Olaf last updated on 22/Mar/21 $$…
Question Number 70898 by Henri Boucatchou last updated on 09/Oct/19 $$\boldsymbol{{Solve}}\::\: \\ $$$$\left.\mathrm{1}.\right)\:\:\sqrt{\boldsymbol{{x}}−\mathrm{2}}\:+\:\sqrt{\mathrm{4}−\boldsymbol{{x}}}\:=\:\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{6}\boldsymbol{{x}}+\mathrm{11} \\ $$$$\left.\mathrm{2}.\right)\:\:\boldsymbol{{x}}^{\mathrm{4}} \:+\:\boldsymbol{{x}}^{\mathrm{3}} \:−\:\mathrm{2}\boldsymbol{{ax}}^{\mathrm{2}} \:−\:\boldsymbol{{ax}}\:+\:\boldsymbol{{a}}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$ Answered by MJS…
Question Number 5357 by Junaid Mirza last updated on 11/May/16 Commented by Yozzii last updated on 11/May/16 $${Let}\:{the}\:{lowest}\:{position}\:{of}\:{the}\:{bob}\:{be} \\ $$$${that}\:{where}\:{its}\:{gravitational}\:{potential} \\ $$$${energy}\:{is}\:{zero}.\:{Then},\:{by}\:{the}\:{law}\:{of} \\ $$$${conservation}\:{of}\:{energy}\:{for}\:{the}\:{bob}, \\…
Question Number 136425 by Ar Brandon last updated on 21/Mar/21 $$\mathrm{If}\:\alpha>\mathrm{0}\:\mathrm{and}\:\beta>\mathrm{0},\:\mathrm{prove} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{ln}\left(\alpha\mathrm{x}\right)}{\beta^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} }\mathrm{dx}=\frac{\pi}{\mathrm{2}\beta}\mathrm{ln}\left(\alpha\beta\right) \\ $$ Commented by Dwaipayan Shikari last updated…
Question Number 70891 by Henri Boucatchou last updated on 09/Oct/19 $$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\:=\:\boldsymbol{{x}}\left(\boldsymbol{{x}}−\mathrm{1}\right)\left(\boldsymbol{{x}}−\mathrm{2}\right)….\left(\boldsymbol{{x}}−\mathrm{10}\right) \\ $$$$\boldsymbol{{f}}\:'\left(\mathrm{0}\right)\:=\:? \\ $$ Commented by kaivan.ahmadi last updated on 09/Oct/19 $${let}\:{g}\left({x}\right)=\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)…\left({x}−\mathrm{10}\right)\Rightarrow{f}\left({x}\right)={xg}\left({x}\right) \\ $$$$\Rightarrow{f}'\left({x}\right)={g}\left({x}\right)+{xg}'\left({x}\right)\Rightarrow…
Question Number 5354 by Rasheed Soomro last updated on 11/May/16 Commented by Rasheed Soomro last updated on 11/May/16 $$\mathrm{ABCD}\:\mathrm{and}\:\mathrm{EFGH}\:\mathrm{are}\:\mathrm{squares}\:\mathrm{in} \\ $$$$\mathrm{above}\:\mathrm{figure}.\mathrm{The}\:\mathrm{centres}\:\mathrm{of}\:\mathrm{the}\:\:\mathrm{arcs}\: \\ $$$$\mathrm{are}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{the}\:\mathrm{external}\:\mathrm{square}. \\ $$$$\mathrm{If}\:\:\mathrm{EF}=\mathrm{t}\:\mathrm{then}\:\mathrm{AB}=?…
Question Number 70886 by Omer Alattas last updated on 09/Oct/19 Commented by mathmax by abdo last updated on 10/Oct/19 $$\mathrm{1}−{cosu}\:\sim\frac{{u}^{\mathrm{2}} }{\mathrm{2}}\:{and}\:{sinu}\:\sim\:{u}\:{if}\:{u}\in{V}\left(\mathrm{0}\right)\:\Rightarrow \\ $$$$\mathrm{1}−{cos}\left(\frac{\pi{t}}{\mathrm{3}}\right)\sim\frac{\left(\frac{\pi{t}}{\mathrm{3}}\right)^{\mathrm{2}} }{\mathrm{2}}\:=\pi^{\mathrm{2}} \frac{{t}^{\mathrm{2}}…