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Author: Tinku Tara

u-R-2-R-u-x-u-y-x-y-u-xy-

Question Number 324 by 123456 last updated on 25/Jan/15 $${u}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\frac{\partial{u}}{\partial{x}}+\frac{\partial{u}}{\partial{y}}=\frac{\left({x}+{y}\right){u}}{{xy}} \\ $$ Answered by prakash jain last updated on 21/Dec/14 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{symmetric}\:\mathrm{in}\:{x},{y}. \\…

Question-65858

Question Number 65858 by ugwu Kingsley last updated on 05/Aug/19 Commented by mathmax by abdo last updated on 05/Aug/19 $${x}+\mathrm{2}{y}^{'} \:+{y}\:=\left({x}+\mathrm{2}\right)^{\mathrm{3}} \:\Rightarrow\mathrm{2}{y}^{'} \:+{y}\:=\left({x}+\mathrm{2}\right)^{\mathrm{3}} −{x}\:\Rightarrow \\…

lim-x-4-2x-2-16-4-4x-2-16x-1-2x-2-16-4-

Question Number 131388 by Eric002 last updated on 04/Feb/21 $$\underset{{x}\rightarrow\mathrm{4}} {{lim}}\frac{\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{16}}+\mathrm{4}}{\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{16}}−\mathrm{4}} \\ $$ Answered by bemath last updated on 04/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{4}} {\mathrm{lim}}\left(\frac{\sqrt{\mathrm{2}{x}^{\mathrm{2}}…

f-R-R-g-R-R-f-x-determinant-x-g-x-g-x-x-g-x-determinant-f-x-x-x-f-x-

Question Number 316 by 123456 last updated on 25/Jan/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)=\begin{vmatrix}{{x}}&{{g}\left({x}\right)}\\{{g}\left(−{x}\right)}&{−{x}}\end{vmatrix} \\ $$$${g}\left({x}\right)=\begin{vmatrix}{{f}\left({x}\right)}&{{x}}\\{−{x}}&{{f}\left(−{x}\right)}\end{vmatrix} \\ $$ Answered by prakash jain last updated on…

lim-x-x-5-cos-1-pix-2-x-6-sin-1-pix-7-x-5-6-x-7-

Question Number 131386 by bemath last updated on 04/Feb/21 $$\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{{x}^{\mathrm{5}} \:\mathrm{cos}\:\left(\frac{\mathrm{1}}{\pi{x}^{\mathrm{2}} }\right)+{x}^{\mathrm{6}} \:\mathrm{sin}\:\left(\frac{\mathrm{1}}{\pi{x}}\right)+\:\mathrm{7}}{\mid{x}\mid^{\mathrm{5}} +\mathrm{6}\mid{x}\mid+\mathrm{7}}=? \\ $$ Answered by liberty last updated on 04/Feb/21 $$\:\underset{{x}\rightarrow−\infty}…