Question Number 87625 by M±th+et£s last updated on 05/Apr/20 $${if}\:{f}\left({x}\right)={sin}^{−\mathrm{1}} \left({cos}\left[{x}\right]\right) \\ $$$${find}\:{Df}\:{and}\:\:{Rf}\:{the}\:{function} \\ $$$$ \\ $$$${notice}/\:\left[…\right]\:{is}\:{floor} \\ $$ Answered by mind is power last…
Question Number 153153 by liberty last updated on 05/Sep/21 Answered by mr W last updated on 05/Sep/21 $$\left(\mathrm{1}\right) \\ $$$${a}+{b}+{c}=\mathrm{4} \\ $$$$\left({a}+{b}+{c}\right)^{\mathrm{2}} ={a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}}…
Question Number 153152 by puissant last updated on 05/Sep/21 $$\int\:\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx} \\ $$ Answered by peter frank last updated on 05/Sep/21 $$\mathrm{u}=\sqrt{\mathrm{x}^{\mathrm{3}} +\mathrm{1}} \\ $$$$\mathrm{u}^{\mathrm{2}}…
Question Number 22082 by Tinkutara last updated on 10/Oct/17 $$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{a}\:\mathrm{fifty}-\mathrm{element}\:\mathrm{subset}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set} \\ $$$$\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:….,\:\mathrm{100}\right\}\:\mathrm{such}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two} \\ $$$$\mathrm{numbers}\:\mathrm{from}\:{A}\:\mathrm{add}\:\mathrm{up}\:\mathrm{to}\:\mathrm{100}\:\mathrm{show} \\ $$$$\mathrm{that}\:{A}\:\mathrm{contains}\:\mathrm{a}\:\mathrm{square}. \\ $$ Answered by Rasheed.Sindhi last updated on 14/Oct/17…
Question Number 153154 by liberty last updated on 05/Sep/21 $$\:\:\underset{{x}\rightarrow{y}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({e}^{{x}} \right)−\mathrm{sin}\:\left({e}^{{y}} \right)}{{x}−{y}}=? \\ $$ Answered by bramlexs22 last updated on 05/Sep/21 $$\:\:\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{e}^{\mathrm{x}} \right)−\mathrm{sin}\:\left(\mathrm{e}^{\mathrm{y}}…
Question Number 22080 by Tinkutara last updated on 10/Oct/17 $$\mathrm{Given}\:\mathrm{any}\:\mathrm{positive}\:\mathrm{integer}\:{n}\:\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{rational} \\ $$$$\mathrm{numbers}\:{a}\:\mathrm{and}\:{b},\:{a}\:\neq\:{b},\:\mathrm{which}\:\mathrm{are}\:\mathrm{not} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{which}\:\mathrm{are}\:\mathrm{such}\:\mathrm{that}\:{a}\:−\:{b}, \\ $$$${a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} ,\:{a}^{\mathrm{3}} \:−\:{b}^{\mathrm{3}} ,\:…..,\:{a}^{{n}} \:−\:{b}^{{n}} \:\mathrm{are}\:\mathrm{all} \\…
Question Number 87614 by mary_ last updated on 05/Apr/20 $$\begin{cases}{\left({x}+{y}\right).\mathrm{2}^{{y}−\mathrm{2}{x}} =\mathrm{6}.\mathrm{25}}\\{\left({x}+{y}\right)^{\frac{\mathrm{1}}{\mathrm{2}{x}−{y}}} =\mathrm{5}}\end{cases} \\ $$ Answered by mahdi last updated on 05/Apr/20 $$\left(\mathrm{x}+\mathrm{y}\right)^{\frac{\mathrm{1}}{\mathrm{2x}−\mathrm{y}}} =\mathrm{5}\Rightarrow\left(\mathrm{x}+\mathrm{y}\right)=\mathrm{5}^{\mathrm{2x}−\mathrm{y}} \\ $$$$\left(\mathrm{x}+\mathrm{y}\right).\mathrm{2}^{\mathrm{y}−\mathrm{2x}}…
Question Number 22079 by Tinkutara last updated on 10/Oct/17 $$\mathrm{Let}\:{ABC}\:\mathrm{be}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{and}\:{h}_{{a}} \:\mathrm{the} \\ $$$$\mathrm{altitude}\:\mathrm{through}\:{A}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\left({b}\:+\:{c}\right)^{\mathrm{2}} \:\geqslant\:{a}^{\mathrm{2}} \:+\:\mathrm{4}{h}_{{a}} ^{\mathrm{2}} . \\ $$$$\left(\mathrm{As}\:\mathrm{usual}\:{a},\:{b},\:{c}\:\mathrm{denote}\:\mathrm{the}\:\mathrm{sides}\:{BC},\right. \\ $$$$\left.{CA},\:{AB}\:\mathrm{respectively}.\right) \\ $$…
Question Number 153151 by puissant last updated on 05/Sep/21 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}^{\mathrm{3}} +\mathrm{1}\right)}{{x}+\mathrm{1}}{dx} \\ $$ Answered by Ar Brandon last updated on 05/Sep/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 87613 by mary_ last updated on 05/Apr/20 Commented by TANMAY PANACEA. last updated on 05/Apr/20 $${pls}\:{recheck}\:{question}… \\ $$ Answered by mind is power…