Oblicz granice

[peresbmw]

Obliczyć granice
\( \Lim_{n\to \infty } \frac{ \sqrt[n]{8n^9-2n^3 +4n} }{ \sqrt[n]{2^n+3^n} } \)

[eresh]

Obliczyć granice
\( \Lim_{n\to \infty } \frac{ \sqrt[n]{8n^9-2n^3 +4n} }{ \sqrt[n]{2^n+3^n} } \)

\(\Lim_{n\to \infty } \frac{ \sqrt[n]{8n^9-2n^3 +4n} }{ \sqrt[n]{2^n+3^n} }=\Lim_{n\to\infty}\frac{\sqrt[n]{n^9(8-\frac{2}{n^6}+\frac{4}{n^7})}}{\sqrt[n]{3^n((\frac{2}{3})^n+1)}}=\Lim_{n\to\infty}\frac{(n^{\frac{1}{n}})^9(8-\frac{2}{n^6}+\frac{4}{n^7})^{\frac{1}{n}}}{3\sqrt[n]{((\frac{2}{3})^n+1)}}=\frac{1\cdot 8^0}{3}=\frac{1}{3}\)