Question Number 187607 by SonGoku last updated on 19/Feb/23
![Help! :( Should i partially differentiate the numerator and denominator? lim_((x, y)→(0,1)) [((x^e + ln((1/y)))/(x^e − ln((1/y))))]](https://www.tinkutara.com/question/Q187607.png)
$$\: \\ $$$$\:\boldsymbol{\mathrm{Help}}!\:\::\left(\right. \\ $$$$\: \\ $$$$\:\boldsymbol{\mathrm{Should}}\:\:\boldsymbol{\mathrm{i}}\:\:\boldsymbol{\mathrm{partially}}\:\:\boldsymbol{\mathrm{differentiate}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{numerator}}\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{denominator}}? \\ $$$$\: \\ $$$$\:\underset{\left(\boldsymbol{{x}},\:\boldsymbol{\mathrm{y}}\right)\rightarrow\left(\mathrm{0},\mathrm{1}\right)} {\boldsymbol{\mathrm{lim}}}\left[\frac{\boldsymbol{{x}}^{\boldsymbol{{e}}} \:\:+\:\boldsymbol{{ln}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}{\boldsymbol{{x}}^{\boldsymbol{{e}}} \:−\:\boldsymbol{{ln}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}}\right)}\right] \\ $$
Commented by Ar Brandon last updated on 19/Feb/23
$$\mathrm{Use}\:\mathrm{the}\:\mathrm{kaioken}\:\mathrm{technique}.\:\mathrm{Haha}\:! \\ $$