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Question Number 141685 by mnjuly1970 last updated on 22/May/21 $$\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:……{nice}\:…\:…\:…\:{calculus}….. \\ $$$$\:\:\mathrm{I}{f}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{tan}\left({x}\right)}{{x}}\:=\:\mathrm{1}\:,\:{prove}\:{that}: \\ $$$$\:\:\:\:\:\:\:\:{lim}\frac{\mathrm{1}}{{x}}\left(\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{tan}\left({x}\right)}\right)=\frac{\mathrm{1}}{\mathrm{3}} \\ $$ Answered by iloveisrael last updated on…
Question Number 76151 by Rio Michael last updated on 24/Dec/19 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{{k}} {e}^{−\mathrm{4}{x}} ,\:{k}>\mathrm{0} \\ $$ Commented by kaivan.ahmadi last updated on 24/Dec/19 $${lim}_{{x}−\rightarrow\infty} \frac{{x}^{{k}}…
Question Number 10612 by FilupS last updated on 20/Feb/17 Commented by FilupS last updated on 20/Feb/17 $$\mathrm{Solve}\:\mathrm{for}\:\boldsymbol{{A}}'\:\mathrm{and}\:\boldsymbol{{B}}'\:\mathrm{via}: \\ $$$$\mathrm{1}.\:\:\mathrm{Vectors} \\ $$$$\mathrm{2}.\:\:\mathrm{Triganometry} \\ $$ Answered by…
Question Number 141681 by ZiYangLee last updated on 22/May/21 $$\mathrm{On}\:\mathrm{the}\:\mathrm{Argand}\:\mathrm{Diagram},\:\mathrm{the}\:\mathrm{variable}\:\mathrm{point} \\ $$$$\mathrm{Z}\:\mathrm{represents}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:{z}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{a}\:\mathrm{point} \\ $$$$\mathrm{Z}\:\mathrm{which}\:\mathrm{moves}\:\mathrm{such}\:\mathrm{that}\:\mid\frac{{z}−\mathrm{1}}{{z}+\mathrm{2}}\mid=\mathrm{2} \\ $$ Answered by MJS_new last updated on 22/May/21…
Question Number 76146 by john santuy last updated on 24/Dec/19 Commented by john santuy last updated on 24/Dec/19 $${how}\:{to}\:{proof}? \\ $$ Commented by mr W…
Question Number 10607 by Saham last updated on 19/Feb/17 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}: \\ $$$$\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:−\:\mathrm{5x}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by mrW1 last updated on 20/Feb/17 $${a}=\mathrm{2} \\…
Question Number 76143 by Master last updated on 24/Dec/19 Commented by mathmax by abdo last updated on 24/Dec/19 $${let}\:{I}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{4}+{x}^{\mathrm{2}} }{dx}\:\:{changement}\:{x}=\mathrm{2}{sh}\left({t}\right)\:{give} \\ $$$${I}\:=\int_{\mathrm{0}} ^{{argsh}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)}…
Question Number 141672 by iloveisrael last updated on 22/May/21 $$\:\:{Solve}\:{the}\:{equation}\: \\ $$$$\:\:{x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} +\mathrm{10}{x}−\mathrm{3}=\mathrm{0} \\ $$ Answered by MJS_new last updated on 22/May/21 $$\left({x}^{\mathrm{2}}…
Question Number 141669 by bramlexs22 last updated on 22/May/21 Answered by iloveisrael last updated on 22/May/21 $$\left({i}\right)\:{f}\left({a}\right)={g}\left({a}\right)\:,{a}>\mathrm{0} \\ $$$$\Rightarrow\:{a}+\mid\mathrm{2}{a}\mid\:=\:−{a}^{\mathrm{2}} −\frac{\mathrm{2}}{\mathrm{3}}{a}+\frac{\mathrm{14}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{3}{a}\:=−{a}^{\mathrm{2}} −\frac{\mathrm{2}}{\mathrm{3}}{a}+\frac{\mathrm{14}}{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{3}{a}^{\mathrm{2}}…