Question Number 76919 by jagoll last updated on 01/Jan/20 $${what}\:{range}\: \\ $$$${the}\:{function}\:{y}\:=\:\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +{x}}}\:? \\ $$ Answered by MJS last updated on 01/Jan/20 $$\mathrm{defined}\:\mathrm{for}\:−\infty<{x}<−\mathrm{1}\vee\mathrm{0}<{x}<+\infty \\ $$$$\frac{{d}}{{dx}}\left[\frac{{x}−\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 11382 by tawa last updated on 22/Mar/17 $$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{24}\:\mathrm{different}\:\mathrm{articles}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups}\:\mathrm{of} \\ $$$$\mathrm{12},\:\mathrm{8}\:\mathrm{and}\:\mathrm{4}\:\mathrm{articles}\:\mathrm{respectively} \\ $$ Commented by sandy_suhendra last updated on 23/Mar/17 $$\mathrm{24C12}\:×\:\mathrm{12C8}\:×\:\mathrm{4C4} \\ $$ Commented…
Question Number 76917 by naka3546 last updated on 01/Jan/20 Commented by MJS last updated on 01/Jan/20 $$\mathrm{just}\:\mathrm{guessing}:\:\mathrm{65563}=\mathrm{4}^{\mathrm{8}} +\mathrm{3}^{\mathrm{3}} \\ $$ Commented by MJS last updated…
Question Number 76913 by Ajao yinka last updated on 31/Dec/19 Answered by ~blr237~ last updated on 01/Jan/20 $$\mathrm{let}\:\mathrm{it}\:\mathrm{be}\:\mathrm{A} \\ $$$$\mathrm{1}+\mathrm{x}+….+\mathrm{x}^{\mathrm{100}} =\frac{\mathrm{1}−\mathrm{x}^{\mathrm{101}} }{\mathrm{1}−\mathrm{x}} \\ $$$$\mathrm{A}=\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 76910 by aliesam last updated on 31/Dec/19 Commented by MJS last updated on 31/Dec/19 $${x}^{\mathrm{6}} +\mathrm{1}=\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\sqrt{\mathrm{3}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} −\sqrt{\mathrm{3}}{x}+\mathrm{1}\right) \\ $$ Answered by…
Question Number 142444 by mathdanisur last updated on 31/May/21 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {{lim}}\:\frac{{tan}^{\mathrm{2}} {x}−\sqrt{\mathrm{3}}{tanx}}{{cos}\left({x}+\frac{\pi}{\mathrm{6}}\right)}=? \\ $$ Answered by bramlexs22 last updated on 31/May/21 $$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:^{\mathrm{2}} {x}−\sqrt{\mathrm{3}}\:\mathrm{tan}\:{x}}{\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{6}}\right)}\:=? \\…
Question Number 142447 by ajfour last updated on 31/May/21 Commented by ajfour last updated on 31/May/21 $${Find}\:{ellipse}\:{perimeter}. \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 11373 by ketto last updated on 22/Mar/17 Answered by sm3l2996 last updated on 22/Mar/17 $$\overset{−} {\mathrm{D}}\overset{\rightarrow} {\mathrm{F}}=\mathrm{D}\overset{\rightarrow} {\mathrm{A}}+\mathrm{A}\overset{\rightarrow} {\mathrm{B}}+\mathrm{B}\overset{\rightarrow} {\mathrm{F}} \\ $$$$\mathrm{DF}=\sqrt{\mathrm{DA}^{\mathrm{2}} +\mathrm{AB}^{\mathrm{2}}…
Question Number 11372 by agni5 last updated on 22/Mar/17 $$\mathrm{If}\:\mathrm{G}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{G}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{groups}\:,\:\mathrm{and}\:\mathrm{f}\::\:\mathrm{G}_{\mathrm{1}} \:\rightarrow\mathrm{G}_{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{group}\:\mathrm{homomorphism}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{o}\left(\mathrm{G}_{\mathrm{1}} \right)\:=\:\mathrm{o}\left(\mathrm{G}_{\mathrm{2}} \right)\:. \\ $$ Terms of Service Privacy…
Question Number 142443 by Hassen_Timol last updated on 31/May/21 $$\:\:\:\:\:\:{F}\left({x}\right)\:=\:\int_{\:{x}} ^{\:\:{x}^{\mathrm{2}} } \frac{\mathrm{1}}{\:\mathrm{ln}\left({t}\right)\:}\:\mathrm{d}{t} \\ $$$$\:\:\mathrm{Show}\:\mathrm{that}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid\:{F}\left({x}\right)\:\mid\:\:\leqslant\:\:\frac{\mid\:{x}^{\mathrm{2}} \:−\:{x}\:\mid}{\mid\:\mathrm{ln}\left({x}\right)\:\mid} \\ $$$$ \\ $$$$\mathrm{Please} \\ $$ Answered…