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…
Question Number 76904 by mpsicasa last updated on 31/Dec/19 $$\mathrm{montrer}\:\mathrm{que}: \\ $$$$\forall{x},{y},{z}>\mathrm{0}\:\:{x}^{\mathrm{3}} +\mathrm{2}{y}^{\mathrm{2}} +\mathrm{4}{z}\geqslant\mathrm{6}{xy}^{\mathrm{2}/\mathrm{3}} {z}^{\mathrm{1}/\mathrm{3}} \\ $$ Commented by mr W last updated on 31/Dec/19…
Question Number 142437 by mohammad17 last updated on 31/May/21 Answered by Dwaipayan Shikari last updated on 31/May/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\sqrt{\frac{{n}}{{n}+{r}}}\: \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}{dx}\:\:\:\:\mathrm{1}+{x}={u}^{\mathrm{2}}…
Question Number 11365 by agni5 last updated on 22/Mar/17 $$\emptyset\left(\mathrm{n}\right)=\mathrm{n}−\mathrm{1}\:,\:\mathrm{n}\in\mathrm{Z}\:,\mathrm{where}\:\emptyset\:\mathrm{is}\:\mathrm{Eular}\:\mathrm{phi}\:\mathrm{function}. \\ $$$$\mathrm{True}\:\mathrm{or}\:\mathrm{false}\:.\mathrm{And}\:\mathrm{explain}\:\mathrm{it}\:. \\ $$ Commented by bahmanfeshki1 last updated on 22/Mar/17 $${if}\:{n}\:{be}\:{prime}\:{number}\:{is}\:{true}\:{otherwise} \\ $$$${is}\:{false} \\…