Question Number 132531 by bemath last updated on 15/Feb/21 $$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2sin}\:\mathrm{x}+\mathrm{3}}−\sqrt{\mathrm{sin}\:\mathrm{x}+\mathrm{1}} \\ $$ Answered by liberty last updated on 15/Feb/21 $$\frac{\mathrm{df}\left(\mathrm{x}\right)}{\mathrm{dx}}=\frac{\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{2sin}\:\mathrm{x}+\mathrm{3}}}−\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{2}\sqrt{\mathrm{sin}\:\mathrm{x}+\mathrm{1}}}\:=\mathrm{0} \\ $$$$\:\frac{\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{2sin}\:\mathrm{x}+\mathrm{3}}}\:=\:\frac{\mathrm{cos}\:\mathrm{x}}{\mathrm{2}\sqrt{\mathrm{sin}\:\mathrm{x}+\mathrm{1}}} \\…
Question Number 1456 by 123456 last updated on 06/Aug/15 $$ \mathrm{S}^{\mathrm{1}} =\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} :{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right\} \\ $$$$\varphi:\left[\mathrm{0},\mathrm{4}\pi\right)\rightarrow\mathrm{E}^{\mathrm{1},\mathrm{1}} ,\mathrm{E}^{\mathrm{1},\mathrm{1}} \subset\mathbb{R}^{\mathrm{2}} \\ $$$$\varphi\left({t}\right)=\left(\mathrm{1}+\mathrm{cos}\:{t}\:\mathrm{sin}\:{t}\right)\left(\mathrm{cos}\:{t},\mathrm{sin}\:{t}\right) \\ $$$$\mathrm{S}^{\mathrm{1}} \cap\mathrm{E}^{\mathrm{1},\mathrm{1}} \neq\emptyset…
Question Number 1454 by 123456 last updated on 06/Aug/15 $$\mathrm{lets}\:{f}:\mathbb{R}\rightarrow\mathbb{R},\:\mathrm{if}\:\left({f}\bullet{f}\right)\left({x}\right)\:\mathrm{is}\:\mathrm{continuous} \\ $$$$\mathrm{proof}\:\mathrm{or}\:\mathrm{give}\:\mathrm{a}\:\mathrm{counter}\:\mathrm{example}\:\mathrm{that}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{continous}. \\ $$ Commented by 123456 last updated on 07/Aug/15 $${f}\left({x}\right)=\begin{cases}{\mathrm{3},{x}>\mathrm{0}}\\{\mathrm{2},{x}=\mathrm{0}}\\{\mathrm{1},{x}<\mathrm{0}}\end{cases} \\ $$ Commented…
Question Number 66988 by Mr Jor last updated on 21/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 1453 by 112358 last updated on 06/Aug/15 $${Show}\:{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}{e}^{{rx}} =\frac{{e}^{{x}} \left({e}^{{nx}} −\mathrm{1}\right)}{{e}^{{x}} −\mathrm{1}}\:\:\:\:\:\:\:\left(\ast\right) \\ $$$${if}\:\:\:{e}^{{rx}} ={cos}\left({irx}\right)−{isin}\left({irx}\right)\:{and}\:{x}\neq\mathrm{0}\:. \\ $$$$\left[{Do}\:{not}\:{treat}\:\left(\ast\right)\:{as}\:{a}\:{GP}\:{to}\right. \\ $$$$\left.{directly}\:{obtain}\:{the}\:{result}.\right]…
Question Number 66986 by Mr Jor last updated on 21/Aug/19 Commented by Mr Jor last updated on 21/Aug/19 $${The}\:{metal}\:{solid}\:{above}\:{is}\:{made}\:{up} \\ $$$${by}\:{joining}\:{a}\:{hemisphere}\:{of}\:{radius} \\ $$$$\mathrm{7}{cm}\:{to}\:{a}\:{cylinder}\:{of}\:{the}\:{same}\:{radius}. \\ $$$${The}\:{mass}\:{and}\:{density}\:{of}\:{the}\:{solid}…
Question Number 66985 by Mr Jor last updated on 21/Aug/19 $$\mathrm{The}\:\mathrm{external}\:\mathrm{length},\mathrm{width}\:\mathrm{and}\:\mathrm{height} \\ $$$$\mathrm{of}\:\mathrm{an}\:\mathrm{open}\:\mathrm{rectangular}\:\mathrm{container}\:\mathrm{are} \\ $$$$\mathrm{41cm},\mathrm{21cm}\:\mathrm{and}\:\mathrm{15}.\mathrm{5cm}\:\mathrm{respectively}. \\ $$$$\mathrm{The}\:\mathrm{thickness}\:\mathrm{of}\:\mathrm{the}\:\mathrm{material}\:\mathrm{making} \\ $$$$\mathrm{the}\:\mathrm{container}\:\mathrm{is}\:\mathrm{5mm}.\mathrm{If}\:\mathrm{the}\:\mathrm{container} \\ $$$$\mathrm{has}\:\mathrm{8litres}\:\mathrm{of}\:\mathrm{water},\mathrm{calculate}\:\mathrm{the} \\ $$$$\mathrm{internal}\:\mathrm{height}\:\mathrm{above}\:\mathrm{the}\:\mathrm{water}\:\mathrm{level}. \\ $$$$\:\:\:\:\:\:\:\:…
Question Number 1448 by 123456 last updated on 05/Aug/15 $$\boldsymbol{{x}}=\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} \right),\boldsymbol{{y}}=\left({y}_{\mathrm{1}} ,{y}_{\mathrm{2}} \right) \\ $$$$\eta:\left[\mathrm{0},\mathrm{1}\right)^{\mathrm{4}} \rightarrow\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\eta\left(\boldsymbol{{x}},\boldsymbol{{y}}\right):=\mathrm{med}\left[\frac{\left(\mathrm{1}−{x}_{\mathrm{1}} \right)^{{y}_{\mathrm{1}} } +\left(\mathrm{1}−{y}_{\mathrm{1}} \right)^{{x}_{\mathrm{1}} } }{\mathrm{2}},\frac{\left(\mathrm{1}−{x}_{\mathrm{2}}…
Question Number 132519 by mnjuly1970 last updated on 14/Feb/21 $$\:\:\:\:\:….\:\:{nice}\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} {ln}\left({n}\right)}{{n}}=\gamma{ln}\left(\mathrm{2}\right)−\frac{\mathrm{1}}{\mathrm{2}}{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$$$ \\ $$ Answered by mindispower…
Question Number 66980 by Mr Jor last updated on 21/Aug/19 Commented by Mr Jor last updated on 21/Aug/19 $${The}\:{figure}\:{above}\:{is}\:{a}\:{right}\:{pyramid} \\ $$$${with}\:{a}\:{rectangular}\:{base}\:{ABCD}\:{and} \\ $$$${VO}\:{as}\:{the}\:{height}. \\ $$$${The}\:{vectors}\:\boldsymbol{{AD}}=\boldsymbol{{a}},\boldsymbol{{AB}}=\boldsymbol{{b}}\:{and}\:\boldsymbol{{DV}}=\boldsymbol{{c}}…