Question Number 136827 by otchereabdullai@gmail.com last updated on 26/Mar/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{values}\:\mathrm{of}:\: \\ $$$$\left.\mathrm{1}\right)\:\mathrm{y}=\mathrm{5sinx}\:\mathrm{2cosx} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{y}=\mathrm{sin}^{\mathrm{2}} \mathrm{x}+\mathrm{3cos}^{\mathrm{2}} \mathrm{x} \\ $$ Commented by mr W last…
Question Number 136783 by Abdoulaye last updated on 26/Mar/21 $${a},{b}\in{R} \\ $$$$\left({a}+{b}\right)^{{n}} =\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}{a}^{{k}} {b}^{{n}−{k}} \\ $$$${demontration}! \\ $$ Commented by mr W last…
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Question Number 136765 by Ñï= last updated on 25/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({x}+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\right)}{{x}}{dx}=\frac{\pi^{\mathrm{2}} }{\mathrm{16}} \\ $$ Answered by snipers237 last updated on 25/Mar/21 $${let}\:{named}\:{it}\:{A} \\…
Question Number 71229 by naka3546 last updated on 13/Oct/19 Commented by naka3546 last updated on 13/Oct/19 $${Difference}\:\:{of}\:\:{red}\:\:{area}\:\:{and}\:\:{blue}\:\:{area}\:\:{is}\:\:… \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 5692 by FilupSmith last updated on 24/May/16 $${f}\left({x}\right)={e}^{{x}} \\ $$$${g}\left({x}\right)=\mathrm{ln}\:{x} \\ $$$${h}\left({x}\right)={x} \\ $$$$ \\ $$$$\mathrm{A}\:\mathrm{line}\:{L}\:\mathrm{is}\:\mathrm{perpendicular}\:\mathrm{to}\:{h}\left({x}\right)\:\mathrm{at}\:\mathrm{point} \\ $$$${P}\left({x},{y}\right)\:\mathrm{and}\:\mathrm{extends}\:\mathrm{and}\:\mathrm{disects}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right). \\ $$$$\mathrm{The}\:\mathrm{length}\:\mathrm{of}\:{L}\:\mathrm{between}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right) \\ $$$$\mathrm{is}\:{r}.\:\mathrm{When}\:\mathrm{is}\:{r}\:\mathrm{minimum}? \\…
Question Number 136745 by PGeeman last updated on 25/Mar/21 Commented by mr W last updated on 25/Mar/21 $${the}\:“{forum}\:{user}\:{id}''\:{from}\:{you}\:{is} \\ $$$${PGeeman}\:{for}\:{example}. \\ $$ Terms of Service…
Question Number 71206 by naka3546 last updated on 13/Oct/19 $${Let}\:\:{p},{q},{r}\:\:{are}\:\:{positive}\:\:{real}\:\:{numbers}\:. \\ $$$$\mathrm{0}\:<\:{r}\:<\:{min}\left\{{p},{q}\right\}. \\ $$$${Prove}\:\:{that} \\ $$$$\:\:\:\:\:\sqrt{{p}−{r}}\:+\:\sqrt{{q}−{r}}\:\:\leqslant\:\:{min}\left\{\sqrt{\frac{{pq}}{{r}}}\:,\:\sqrt{\mathrm{2}\left({p}+{q}\:−\:\mathrm{2}{r}\right)}\:\right\} \\ $$ Answered by mind is power last updated…
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Question Number 136733 by Ñï= last updated on 25/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\frac{\mathrm{1}}{\mathrm{4}^{{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }=\frac{\pi^{\mathrm{3}} }{\mathrm{48}}+\frac{\pi}{\mathrm{4}}{ln}^{\mathrm{2}} \mathrm{2} \\ $$ Answered by mindispower last updated on 25/Mar/21…