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Question Number 173190 by mathlove last updated on 08/Jul/22

$$\underset{x\to 0}{\lim }\frac{ln(2-e^x)}{x+lnx}=?$$

Answered by thfchristopher last updated on 08/Jul/22

$$=\underset{x\to 0}{\lim }\frac{\frac{-e^x}{2-e^x}}{1+\frac{1}{x}}$$$$=\underset{x\to 0}{\lim }\frac{-{xe}^x}{(2-e^x)(x+1)}$$$$=0$$

Answered by CElcedricjunior last updated on 08/Jul/22

$$\underset{x\to 0^{+}}{\lim }\frac{\mathbf{ln}(2-{\mathbf{e}}^{\mathbf{x}})}{\mathbf{x}+\mathbf{lnx}}=0$$$$$$$$$$$$.........lec\acute{el}\stackrel{`}{ebre}cedricjunior........$$

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