Oblicz granice

[lukasz93a]

\(\displaystyle{ \lim_{ n\to \infty } \left( \sqrt[4]{n^{4}+16}-n \right)}\)

Jak to policzyć?

[MichalPWr]

\(\displaystyle{ a ^{4}-b ^{4}=\left( a-b\right) \cdot \left( a ^{3} +a ^{2} +ab ^{2}+b ^{3} \right)}\)

[lukasz93a]

\(\displaystyle{ \lim_{ n\to \infty } \left( \frac{16}{ \left( n^{4}+16\right) ^{ \frac{3}{4} } +\left( n^{4}+16\right) ^{ \frac{2}{4} }+256\left( n^{4}+16\right) ^{ \frac{1}{4} }+4096} \right)}\)

Dobrze liczę?

[MichalPWr]

lukasz93a, Źle, \(\displaystyle{ a=\sqrt[4]{n^{4}+16} \ \ b=n}\).