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Question Number 91813 by jagoll last updated on 03/May/20

$$\underset{x\to 1}{\lim }\frac{1-x+\ln x}{1-\sqrt{2x-x^2}}?$$

Commented by john santu last updated on 03/May/20

$$L^{\prime }Hopital$$$$\underset{x\to 1}{\lim }\frac{-1+\frac{1}{x}}{-\left(\frac{2-2x}{2\sqrt{2x-x^2}}\right)}=$$$$\underset{x\to 1}{\lim }\frac{(1-x)2\sqrt{2x-x^2}}{-2x(1-x)}=$$$$\underset{x\to 1}{\lim }\frac{-\sqrt{2x-x^2}}{x}=-1$$

Commented by john santu last updated on 03/May/20

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Commented by jagoll last updated on 03/May/20

$$\mathrm{thank}\mathrm{you}\mathrm{sir}$$

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