Question Number 136186 by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Let}\:{f}\left({x}\right)=\mathrm{cos}^{−\mathrm{1}} {x}+\mathrm{cos}^{−\mathrm{1}} \left({x}−\mathrm{1}\right),\: \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{f}. \\ $$ Answered by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Ans}:\:\left[\frac{\pi}{\mathrm{2}},\frac{\mathrm{3}\pi}{\mathrm{2}}\right] \\…
Question Number 5111 by LMTV last updated on 13/Apr/16 $$\int\frac{{dy}}{{e}^{{y}} }=? \\ $$ Answered by FilupSmith last updated on 13/Apr/16 $$=\int{e}^{−{y}} {dy} \\ $$$$\int{e}^{{ax}+{b}} {dx}={ae}^{{ax}+{b}}…
Question Number 70638 by abdusalamyussif@gmail.com last updated on 06/Oct/19 Commented by MJS last updated on 06/Oct/19 $$\mathrm{the}\:\mathrm{first}\:\mathrm{question}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{complete} \\ $$ Answered by mr W last updated…
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Question Number 5100 by LMTV last updated on 12/Apr/16 $$\int\frac{{dy}}{\mathrm{1}+{y}^{\mathrm{2}} }=\mathrm{tan}^{−\mathrm{1}} {y}+{c} \\ $$$$\mathrm{why}??\:\mathrm{and} \\ $$$$\int\frac{{dy}}{\mathrm{1}−{y}^{\mathrm{2}} }=? \\ $$ Answered by Yozzii last updated on…
Question Number 5097 by LMTV last updated on 12/Apr/16 $${x}^{\mathrm{2}} {y}'={x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} \\ $$$${yy}'+\mathrm{sin}\:{x}=\mathrm{0} \\ $$$${y}'=\mathrm{1}−{y}^{\mathrm{2}} \\ $$$$\mathrm{separation}\:\mathrm{of}\:\mathrm{variables} \\ $$ Answered by Yozzii last updated…
Question Number 136170 by mnjuly1970 last updated on 19/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:…..{nice}\:\:{calculus}…. \\ $$$$\:\:\:{compute}:: \\ $$$$\mathrm{2}{li}_{\mathrm{2}} \left(\frac{−\mathrm{1}}{\mathrm{2}}\right)−\mathrm{2}{li}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)+{li}_{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)=?? \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 136165 by bramlexs22 last updated on 19/Mar/21 $${Find}\:{the}\:{equation}\:{of}\:{ellipse}\:{with} \\ $$$${F}_{\mathrm{1}} \left(\mathrm{1},\mathrm{2}\right)\:,\:{F}_{\mathrm{2}} \left(\mathrm{3},\mathrm{4}\right)\:{and}\:\mathrm{2}{a}\:=\:\mathrm{2}\sqrt{\mathrm{3}} \\ $$ Commented by bramlexs22 last updated on 19/Mar/21 $${Dear}\:{Mr}\:{W}\:{can}\:{you}\:{help}\:{me} \\…
Question Number 136167 by ZiYangLee last updated on 19/Mar/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{value}\:\mathrm{for}\:\mathrm{the}\:\mathrm{5}^{\mathrm{th}} \\ $$$$\mathrm{root}\:\mathrm{of}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{is}\:−\mathrm{1}+{i}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{another}\:\mathrm{four}\:\mathrm{values}. \\ $$ Answered by mr W last updated on 19/Mar/21 $${one}\:\mathrm{5}^{{th}}…
Question Number 136161 by nimnim last updated on 19/Mar/21 $${How}\:{do}\:{I}\:{find}\:{the}\:{sum}\:{of} \\ $$$$\:\:\mathrm{1}+\mathrm{3}{x}+\mathrm{6}{x}^{\mathrm{2}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{15}{x}^{\mathrm{4}} +…….\infty,\:\:{where}\:−\mathrm{1}<{x}<\mathrm{1}\:? \\ $$$$\:\:{Please}\:{Help}.. \\ $$ Answered by bramlexs22 last updated on…