Question Number 115732 by gab last updated on 28/Sep/20 Commented by Dwaipayan Shikari last updated on 28/Sep/20 $$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }{\mathrm{2n}^{\mathrm{2}} }\mathrm{e}^{\pi\mathrm{in}} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{e}^{\mathrm{i}\pi} }{\mathrm{1}^{\mathrm{2}}…
Question Number 181245 by Mastermind last updated on 23/Nov/22 $$\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)\left(\mathrm{x}^{\frac{\mathrm{4}}{\mathrm{3}}} +\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \right)=\mathrm{x}^{\frac{\mathrm{1}}{\mathrm{3}}} \left(\mathrm{x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\right) \\ $$$$ \\ $$$$\mathrm{prove}\:\mathrm{LHS}=\mathrm{RHS} \\ $$ Commented by Socracious last…
Question Number 115696 by Dwaipayan Shikari last updated on 27/Sep/20 $$\mathrm{e}^{\mathrm{x}} =\mathrm{logx} \\ $$ Commented by Dwaipayan Shikari last updated on 27/Sep/20 $$\mathrm{e}^{\mathrm{x}} =\mathrm{logx} \\…
Question Number 181217 by Mastermind last updated on 23/Nov/22 Answered by Rasheed.Sindhi last updated on 23/Nov/22 $$\mathrm{3}^{{x}} \left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} =\mathrm{225}=\mathrm{3}^{\mathrm{2}} \mathrm{5}^{\mathrm{2}} \\ $$$${x}=\mathrm{2}\:\wedge\:\mathrm{2}{x}+\mathrm{1}=\mathrm{5} \\ $$$$\Rightarrow{x}=\mathrm{2}\:\wedge\:\mathrm{2}\left(\mathrm{2}\right)+\mathrm{1}=\mathrm{5} \\…
Question Number 181218 by Mastermind last updated on 23/Nov/22 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Differential}\:\mathrm{equation}: \\ $$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}=\mathrm{2y}\left(\mathrm{lnx}−\mathrm{lny}\right) \\ $$$$ \\ $$$$. \\ $$ Answered by qaz last updated on 23/Nov/22…
Question Number 181219 by Mastermind last updated on 23/Nov/22 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{D}.\mathrm{E} \\ $$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$. \\ $$ Answered by qaz last updated…
Question Number 115632 by m173 last updated on 27/Sep/20 Commented by m173 last updated on 27/Sep/20 find general solution Commented by MJS_new last updated on 27/Sep/20 $${y}={c}\mathrm{sin}\:{x}\:\mathrm{is}\:\mathrm{already}\:\mathrm{the}\:\mathrm{solution}?!…
Question Number 115487 by 171 last updated on 26/Sep/20 Commented by Dwaipayan Shikari last updated on 26/Sep/20 $$\mathrm{y}^{\mathrm{2}} =\mathrm{1}+\mathrm{1}\:\left(\mathrm{x}=\mathrm{1}\right) \\ $$$$\mathrm{y}=\pm\sqrt{\mathrm{2}} \\ $$$$\mathrm{y}^{\mathrm{2}} =\mathrm{1}+\mathrm{2}\Rightarrow\mathrm{y}=\pm\sqrt{\mathrm{3}} \\…
Question Number 181023 by mnjuly1970 last updated on 20/Nov/22 Answered by mr W last updated on 20/Nov/22 Commented by mr W last updated on 20/Nov/22…
Question Number 181015 by Mastermind last updated on 20/Nov/22 $$\mathrm{If}\:\mathrm{z}=\mathrm{xy}−\mathrm{7x}+\mathrm{4y},\:\:\:\mathrm{evaluate}\:\frac{\partial\mathrm{z}}{\partial\mathrm{x}\:}\:\mathrm{and}\:\frac{\partial\mathrm{z}}{\partial\mathrm{y}} \\ $$$$ \\ $$$$. \\ $$$$ \\ $$ Answered by CrispyXYZ last updated on 20/Nov/22…