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Author: Tinku Tara

Question-68923

Question Number 68923 by ramirez105 last updated on 16/Sep/19 Commented by kaivan.ahmadi last updated on 16/Sep/19 $$\frac{\partial{u}}{\partial{x}}=\frac{\mathrm{1}}{{y}}\Rightarrow{u}\left({x},{y}\right)=\int\frac{\mathrm{1}}{{y}}{dx}=\frac{{x}}{{y}}+{h}\left({y}\right) \\ $$$$\frac{\partial{u}}{\partial{y}}=−\frac{{x}}{{y}^{\mathrm{2}} }=−\frac{{x}}{{y}^{\mathrm{2}} }+\frac{{dh}}{{dy}}\Rightarrow\frac{{dh}}{{dy}}=\mathrm{0}\Rightarrow{h}={c}' \\ $$$$ \\ $$$$\Rightarrow{u}\left({x},{y}\right)={c}\Rightarrow\frac{{x}}{{y}}={c}\Rightarrow{x}−{cy}=\mathrm{0}…

let-S-i-a-n-x-i-prove-or-disprove-that-d-dx-i-a-n-x-i-i-a-n-d-dx-x-i-i-a-n-x-i-

Question Number 3385 by Filup last updated on 12/Dec/15 $$\mathrm{let}: \\ $$$$\:\:\:\:\:\:\:\:{S}=\underset{{i}={a}} {\overset{{n}} {\sum}}{x}_{{i}} \\ $$$$\mathrm{prove}\:\mathrm{or}\:\mathrm{disprove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\frac{{d}}{{dx}}\left(\underset{{i}={a}} {\overset{{n}} {\sum}}{x}_{{i}} \right)=\underset{{i}={a}} {\overset{{n}} {\sum}}\left(\frac{{d}}{{dx}}\left\{{x}_{{i}} \right\}\right) \\…

Question-68912

Question Number 68912 by TawaTawa last updated on 16/Sep/19 Answered by MJS last updated on 17/Sep/19 $$\left(\mathrm{1}\right)\:\:{a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} −\mathrm{7}=\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:\:{b}^{\mathrm{2}} +{bc}+{c}^{\mathrm{2}} −\mathrm{21}=\mathrm{0} \\ $$$$\left(\mathrm{3}\right)\:\:{c}^{\mathrm{2}}…