Question Number 68207 by mr W last updated on 07/Sep/19 $${solve}\:{for}\:{x}\in\mathbb{C} \\ $$$$\mathrm{sin}\:{x}={z}\:\:\:\left({z}={a}+{bi}={re}^{{i}\theta} \right) \\ $$ Commented by mathmax by abdo last updated on 07/Sep/19…
Question Number 68203 by peter frank last updated on 07/Sep/19 Commented by Cmr 237 last updated on 07/Sep/19 $$\eth\mathrm{f}=\frac{\eth\mathrm{f}}{\eth\mathrm{x}}+\frac{\eth\mathrm{f}}{\eth\mathrm{y}}+\frac{\eth\mathrm{f}}{\eth\mathrm{z}} \\ $$$$\:\:\:\:=\mathrm{2xy}+\mathrm{cosh}\left(\mathrm{yz}\right)+\mathrm{x}^{\mathrm{2}} +\mathrm{xzsinh}\left(\mathrm{yz}\right)+\mathrm{xysinh}\left(\mathrm{yz}\right) \\ $$ Commented…
Question Number 133738 by mathlove last updated on 23/Feb/21 Answered by Ar Brandon last updated on 24/Feb/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{ln}\left(\mathrm{3x}+\mathrm{1}\right)}{\mathrm{2x}}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3x}−\frac{\mathrm{9x}^{\mathrm{2}} }{\mathrm{2}}+\epsilon\left(\mathrm{x}\right)}{\mathrm{2x}}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Commented by…
Question Number 133734 by Abdoulaye last updated on 23/Feb/21 $${how}\:{do}\:{we}\:{caculate}\:\int{ln}\left({tanx}\right){dx}\:? \\ $$ Answered by mathmax by abdo last updated on 24/Feb/21 $$\mathrm{f}\left(\mathrm{x}\right)=\int_{\frac{\pi}{\mathrm{4}}} ^{\mathrm{x}} \mathrm{ln}\left(\mathrm{tanx}\right)\mathrm{dx}\:\Rightarrow\mathrm{f}\left(\mathrm{x}\right)=_{\mathrm{tanx}=\mathrm{t}} \:\:\:\int_{\mathrm{1}}…
Question Number 133730 by mr W last updated on 24/Feb/21 Commented by mr W last updated on 23/Feb/21 $${as}\:{Q}\mathrm{133275},\:{but}\:{with}\:{coefficient}\:{of} \\ $$$${restitution}\:\boldsymbol{{e}}\:{for}\:{the}\:{impacts}. \\ $$ Commented by…
Question Number 133725 by Ar Brandon last updated on 23/Feb/21 Commented by Ar Brandon last updated on 23/Feb/21 01:15 AM in India, and 24th February…
Question Number 2655 by Yozzi last updated on 24/Nov/15 $${Prove}\:{by}\:{contradiction}\:{that}\:{there} \\ $$$${are}\:{no}\:{whole}\:{number}\:{solutions}\:\left({x},{y},{z}\right) \\ $$$${to}\:{the}\:{equation}\:{z}^{\mathrm{2}} ={x}^{\mathrm{2}} +{y}^{\mathrm{2}} \\ $$$${where}\:{both}\:{x}\:{and}\:{y}\:{are}\:{odd}. \\ $$ Answered by prakash jain last…
Question Number 68191 by peter frank last updated on 06/Sep/19 Answered by mind is power last updated on 06/Sep/19 $${sin}\left({a}−{b}\right)={sin}\left({a}\right){cos}\left({b}\right)−{cos}\left({a}\right){sin}\left({b}\right) \\ $$$$\frac{{sin}\left({a}−{b}\right)}{{cos}\left({a}\right){cos}\left({b}\right)}={tg}\left({a}\right)−{tg}\left({b}\right) \\ $$$$\Rightarrow\frac{{sin}\left({a}−{b}\right)}{{cos}\left({a}\right){cos}\left({b}\right)}={tg}\left({b}\right)\left({k}−\mathrm{1}\right) \\…
Question Number 68188 by mhmd last updated on 06/Sep/19 $$\sum_{{n}=\mathrm{3}} ^{\propto} \:\mathrm{1}/{n}\left({ln}\:{n}\right)^{\mathrm{2}} \:\:\:{is}\:{the}\:{function}\:{converg}\:{or}\:{diverg}\:?\:{pleas}\:{help}\:{me} \\ $$ Commented by Abdo msup. last updated on 07/Sep/19 $${let}\:\varphi\left({x}\right)\:=\frac{\mathrm{1}}{{x}\left({lnx}\right)^{\mathrm{2}} }\:\:{with}\:\:{x}\geqslant\mathrm{3}\:\:{we}\:{have}…
Question Number 68189 by peter frank last updated on 06/Sep/19 Commented by peter frank last updated on 06/Sep/19 $${Qn}\:\mathrm{9},\:\:\mathrm{10} \\ $$ Commented by mind is…