Question Number 60984 by naka3546 last updated on 28/May/19 $$\frac{{a}}{{a}−{b}}\:\:+\:\:\frac{{b}}{{b}−{c}}\:\:+\:\:\frac{{c}}{{c}−{a}}\:\:=\:\:\mathrm{4} \\ $$$${ab}^{\mathrm{2}} \:+\:{bc}^{\mathrm{2}} \:+\:{abc}\:+\:{ca}^{\mathrm{2}} \:\:=\:\:{a}^{\mathrm{2}} {b}\:+\:{b}^{\mathrm{2}} {c}\:+\:{c}^{\mathrm{2}} {a} \\ $$$$\left(\frac{{a}}{{a}−{b}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{b}}{{b}−{c}}\right)^{\mathrm{3}} \:\:+\:\:\left(\frac{{c}}{{c}−{a}}\right)^{\mathrm{3}} \:\:=\:\:? \\ $$$$…
Question Number 60981 by necx1 last updated on 28/May/19 Commented by Prithwish sen last updated on 28/May/19 $$\mathrm{Let}\: \\ $$$$\mathrm{A}=\mathrm{lim}_{\mathrm{x}\rightarrow\infty} \left(\frac{\mathrm{x}!}{\mathrm{x}^{\mathrm{x}} }\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$$$\therefore\mathrm{lnA}=\mathrm{lim}_{\mathrm{x}\rightarrow\infty} \frac{\mathrm{1}}{\mathrm{x}}\mathrm{ln}\left(\frac{\mathrm{1}.\mathrm{2}.\mathrm{3}………..\mathrm{x}}{\mathrm{x}.\mathrm{x}.\mathrm{x}…………\mathrm{x}}\right)…
Question Number 192054 by cortano12 last updated on 07/May/23 $$\:\:\:\mathrm{If}\:\mathrm{Q}\:=\:\frac{\mathrm{2}−\mathrm{x}}{\mathrm{y}−\mathrm{1}}\:;\:−\mathrm{5}\leqslant\mathrm{x}<−\mathrm{1}\:,\:\mathrm{5}\leqslant\mathrm{y}<\mathrm{6} \\ $$$$\:\:\:\mathrm{Find}\:\mathrm{Q}_{\mathrm{max}} .\: \\ $$ Answered by mehdee42 last updated on 07/May/23 $$−\mathrm{5}\leqslant{x}<−\mathrm{1}\overset{×−\mathrm{1}} {\Rightarrow}\:\mathrm{1}<−{x}\leqslant\mathrm{5}\overset{+\mathrm{2}} {\Rightarrow}\mathrm{3}<\mathrm{2}−{x}\leqslant\mathrm{7}\:\:\left({i}\right)…
Question Number 60980 by Tawa1 last updated on 28/May/19 $$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x},\:\mathrm{y},\:\mathrm{z} \\ $$$$\:\:\:\:\:\mathrm{x}\left(\mathrm{y}\:+\:\mathrm{z}\right)\:=\:\mathrm{33}\:\:\:\:\:\:\:\:…..\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\mathrm{y}\left(\mathrm{z}\:+\:\mathrm{x}\right)\:=\:\mathrm{35}\:\:\:\:\:\:\:\:…..\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\mathrm{z}\left(\mathrm{x}\:+\:\mathrm{y}\right)\:=\:\mathrm{14}\:\:\:\:\:\:\:\:…..\:\left(\mathrm{iii}\right) \\ $$ Commented by Prithwish sen last updated on…
Question Number 192049 by sciencestudentW last updated on 06/May/23 $${fog}\left({x}\right)=\mathrm{4}{x}−\mathrm{1} \\ $$$${g}\left({x}\right)={x}−\mathrm{2} \\ $$$${f}\left({x}\right)=? \\ $$ Answered by AST last updated on 06/May/23 $${f}\left({g}\left({x}\right)\right)=\mathrm{4}{x}−\mathrm{1}\Rightarrow{f}\left({x}−\mathrm{2}\right)=\mathrm{4}\left({x}−\mathrm{2}\right)+\mathrm{7} \\…
Question Number 192048 by sciencestudentW last updated on 06/May/23 $${if}\:{the}\:{combined}\:{function}\:{is}\:{h}\left({x}\right)=\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${then}\:{find}\:{the}\:{tow}\:{other}\:{functions}\:{of}\:{its}. \\ $$ Commented by AST last updated on 07/May/23 $${If}\:“{combined}''\:{here}\:{means}\:{h}\left({x}\right)={f}\left({g}\left({x}\right)\right), \\ $$$${f}\left({x}\right)=\sqrt{{x}},{g}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}}…
Question Number 60976 by maxmathsup by imad last updated on 28/May/19 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{by}\:{use}\:{of}\:{integral}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{2}{cos}\theta\right){d}\theta\:\:. \\ $$ Commented by maxmathsup by imad last…
Question Number 192045 by Safiullah_21 last updated on 06/May/23 $$\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\left(\mathrm{1}+\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)\left(\mathrm{1}+\sqrt[{\mathrm{8}}]{\mathrm{2}}\right)\left(\mathrm{1}+\sqrt[{\mathrm{16}}]{\mathrm{2}}\right)}×\left(\frac{\mathrm{1}−\sqrt[{\mathrm{16}}]{\mathrm{2}}}{\mathrm{1}−\sqrt[{\mathrm{16}}]{\mathrm{2}_{} }}\right) \\ $$$$ \\ $$$$\Rightarrow_{} \frac{\mathrm{1}−\sqrt[{\mathrm{16}}]{\mathrm{2}}}{\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\left(\mathrm{1}+\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)\left(\mathrm{1}+\sqrt[{\mathrm{8}}]{\mathrm{2}}\right)\left(\mathrm{1}−\sqrt[{\mathrm{8}}]{\mathrm{2}}\right)}\Rightarrow\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\left(\mathrm{1}+\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)\left(\mathrm{1}−\sqrt[{\mathrm{4}}]{\mathrm{2}}\right)} \\ $$$$ \\ $$ Terms of Service Privacy Policy…
Question Number 126510 by benjo_mathlover last updated on 21/Dec/20 $$\:\int\:\frac{{dx}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{8}}}\:? \\ $$ Answered by liberty last updated on 21/Dec/20 Answered by Ar Brandon last…
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