Question Number 127414 by MathSh last updated on 29/Dec/20 $${From}\:\mathrm{1}\:{to}\:\mathrm{50}\:\left(\mathrm{1}\:{and}\:\mathrm{50}\:{includes}\right) \\ $$$${fev}\:{n}\:{for}\:\frac{\left({n}^{\mathrm{2}} −\mathrm{1}\right)!}{\left({n}!\right)^{{n}} }\:{full}\:{number} \\ $$ Commented by talminator2856791 last updated on 29/Dec/20 $$\:\mathrm{what}\:\mathrm{is}\:\mathrm{fev}? \\…
Question Number 127400 by mohammad17 last updated on 29/Dec/20 $${prove}\:{that}\::\mid\mid{z}_{\mathrm{1}} \mid−\mid{z}_{\mathrm{2}} \mid\mid\leqslant\mid{z}_{\mathrm{1}} +{z}_{\mathrm{2}} \mid \\ $$ Commented by mohammad17 last updated on 29/Dec/20 $$? \\…
Question Number 192927 by 073 last updated on 31/May/23 Answered by aba last updated on 31/May/23 $$\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{m}} \approx\sqrt{\mathrm{2}\pi\mathrm{n}}\left(\frac{\mathrm{n}}{\mathrm{e}}\right)^{\mathrm{n}} ×\mathrm{n}^{\mathrm{m}} \:\:\wedge\:\left(\mathrm{n}+\mathrm{m}\right)!\approx\sqrt{\mathrm{2}\pi\left(\mathrm{n}+\mathrm{m}\right)}\left(\frac{\mathrm{n}+\mathrm{m}}{\mathrm{e}}\right)^{\mathrm{n}+\mathrm{m}} \\ $$$$\Rightarrow\frac{\mathrm{n}!\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{m}} }{\left(\mathrm{n}+\mathrm{m}\right)!}\approx\frac{\sqrt{\mathrm{2}\pi\mathrm{n}}}{\:\sqrt{\mathrm{2}\pi\left(\mathrm{n}+\mathrm{m}\right)}}×\frac{\mathrm{n}^{\mathrm{n}+\mathrm{m}} }{\mathrm{e}^{\mathrm{n}} }×\frac{\mathrm{e}^{\mathrm{n}+\mathrm{m}}…
Question Number 127366 by mohammad17 last updated on 29/Dec/20 $${Appointed}\:{at}\:{the}\:{nodal}\:{level}\:{of}\:{the}\:{group} \\ $$$$ \\ $$$$\mid{z}+\overset{−} {{z}}\mid^{\mathrm{2}} +\left({z}−\overset{−} {{z}}\right)=\mathrm{4}? \\ $$ Commented by JDamian last updated on…
Question Number 127364 by mohammad17 last updated on 29/Dec/20 $${prove}\:{that}:\:{Arg}\left({log}\left(\mathrm{3}−\mathrm{4}{i}\right)\right)=\frac{\mathrm{1}}{{i}}{log}\left(\frac{\mathrm{3}−\mathrm{4}{i}}{\mathrm{5}}\right) \\ $$$$ \\ $$$${help}\:{me}\:{sir}\:{please} \\ $$ Commented by mohammad17 last updated on 29/Dec/20 $${pleas}\:{help}\:{me}\:? \\…
Question Number 127363 by mohammad17 last updated on 29/Dec/20 $${prove}\:{that}\:{log}\left(−\mathrm{1}\right)^{\mathrm{3}} =\mathrm{3}{log}\left(−\mathrm{1}\right)\:? \\ $$ Commented by mohammad17 last updated on 29/Dec/20 $$????? \\ $$ Commented by…
Question Number 127358 by Fareed last updated on 29/Dec/20 $$ \\ $$$$\mathrm{lim}\left(\frac{\mathrm{a}^{\mathrm{x}+\mathrm{1}} +\mathrm{b}^{\mathrm{x}+\mathrm{1}} +\mathrm{c}^{\mathrm{x}+\mathrm{1}} }{\mathrm{a}+\mathrm{b}+\mathrm{c}}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} =? \\ $$$$\mathrm{x}\Rightarrow\mathrm{0} \\ $$ Answered by Ar Brandon last…
Question Number 61818 by Kunal12588 last updated on 09/Jun/19 $$\mathrm{Find}\:\:\:\frac{{dy}}{{dx}}\:\: \\ $$$${y}\:=\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\right),\:\mathrm{0}<{x}<\mathrm{1} \\ $$ Commented by Prithwish sen last updated on 09/Jun/19…
Question Number 192884 by 073 last updated on 30/May/23 Commented by witcher3 last updated on 03/Jun/23 $$\mathrm{let}\:\mathrm{u}=\mathrm{x}+\mathrm{y},\mathrm{v}=\mathrm{x}−\mathrm{y} \\ $$$$\mathrm{g}\left(\mathrm{u},\mathrm{v}\right)=\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{J}_{\mathrm{g}} =\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:−\frac{\mathrm{1}}{\mathrm{2}}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\end{pmatrix}=\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{u}+\mathrm{v}}\\{\mathrm{u}−\mathrm{v}}\end{pmatrix} \\…
Question Number 192879 by Michaelfaraday last updated on 30/May/23 $${Good}\:{morning} \\ $$$${please}\:{what}\:{book}\:{do}\:{you}\:{recommended} \\ $$$${for}\:{calculus}\:{and}\:{physics}\:{for}\:{undergraduate} \\ $$ Answered by ajfour last updated on 30/May/23 $${Physics}:{Resnick}\:{Halliday}\:{Krane} \\…