Question

Va rog frumos am nevoie

Answer 1

Explicație pas cu pas:

$\lim_{x \rightarrow + \infty } \dfrac{6 \ln x - 4 \ln(x + 1) }{9 \ln x - 5 \ln(x + 1)} =$

$= \lim_{x \rightarrow + \infty } \dfrac{6 - 4 \cdot \frac{ \ln(x + 1)}{\ln x} }{9 - 5 \cdot \frac{ \ln(x + 1)}{\ln x}}$

$= \lim_{x \rightarrow + \infty } \dfrac{6 - 4 \cdot \frac{ \frac{1}{x + 1} }{ \frac{1}{x} } }{9 - 5 \cdot \frac{ \frac{1}{x + 1} }{ \frac{1}{x} } }$

$= \lim_{x \rightarrow + \infty } \dfrac{6 - 4 \cdot \frac{1}{1 + \frac{1}{x} } }{9 - 5 \cdot \frac{1}{ 1 + \frac{1}{x} } }$

$= \dfrac{6 - 4}{9 - 5} = \dfrac{2}{4} = \bf \dfrac{1}{2}$