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Question Number 73552 by Rio Michael last updated on 13/Nov/19

$$evaluate$$$$\underset{x\to +\mathrm{\infty }}{Lim}xln\left(\frac{x+1}{x}\right)$$

Commented by mathmax by abdo last updated on 13/Nov/19

$$wehavexln\left(\frac{x+1}{x}\right)=xln(1+\frac{1}{x})=x(\frac{1}{x}+o\left(\frac{1}{x^2}\right))=1+o\left(\frac{1}{x}\right)(x\to +\mathrm{\infty })$$$$\Rightarrow {lim}_{x\to +\mathrm{\infty }}xln\left(\frac{x+1}{x}\right)=1$$

Answered by ajfour last updated on 13/Nov/19

$$L=\underset{x\to \mathrm{\infty }}{\lim }\frac{\ln (1+\frac{1}{x})}{\left(\frac{1}{x}\right)}=1$$

Commented by Rio Michael last updated on 13/Nov/19

$$thanks$$

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