granica

[enta]

oblicz \(\lim _{x\to \infty }\left(3\log _4\left(2x\right)-\log _4\left(\frac{x+1}{2}\right)-\log _4\left(x+2\right)\right)\)

[Galen]

\(\Lim_{x\to \infty }(log_4(8x^3): \frac{x+1}{2}: \frac{x+2}{1})= \Lim_{x\to \infty }log_4(8x^3 \cdot \frac{2}{x+1} \cdot \frac{1}{x+2})=\\= \Lim_{x\to \infty }log_4( \frac{16x^3}{x^2+3x+2})= \Lim_{x\to \infty } log_4( \frac{16x}{1+ \frac{3}{x}+ \frac{2}{x^2} } )= + \infty\)