Question

Determinati asimptota orizontala catre +infinit a fct f (x)= (1+lnx)/(1-lnx )
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Answer 1

$\lim_{x \to +\infty}\limits{\dfrac{1+lnx}{1-lnx}} \overset{\frac{+\infty}{-\infty}(L'H)}{=} \ \lim_{x \to +\infty}\limits{\dfrac{(1+lnx)'}{(1-lnx)'}} = \lim_{x \to +\infty}\limits{\dfrac{\dfrac{1}{x}}{-\dfrac{1}{x}}} = \\ \\ =\lim_{x \to +\infty}\limits{\dfrac{1}{\not{x}}\cdot \Big(-\dfrac{\not{x}}{1}\Big)} = -1$

$\Rightarrow \boxed{y = -1, asimptota orizontala spre + \infty}$