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Výpočet limity pomocí definice
Z definice zjisti hodnotu limity \( \lim _{n \rightarrow \infty}\left[\cos \left(\pi-\frac{3}{n}\right)-\frac{4}{n}+\frac{n^{2}+3}{n^{3}}\right] \).
\( \lim _{n \rightarrow \infty}\left[\cos \left(\pi-\frac{3}{n}\right)-\frac{4}{n}+\frac{n^{2}+3}{n^{3}}\right]=\frac{1}{2} \)
\( \lim _{n \rightarrow \infty}\left[\cos \left(\pi-\frac{3}{n}\right)-\frac{4}{n}+\frac{n^{2}+3}{n^{3}}\right]=0 \)
\( \lim _{n \rightarrow \infty}\left[\cos \left(\pi-\frac{3}{n}\right)-\frac{4}{n}+\frac{n^{2}+3}{n^{3}}\right]=-1 \)
\( \lim _{n \rightarrow \infty}\left[\cos \left(\pi-\frac{3}{n}\right)-\frac{4}{n}+\frac{n^{2}+3}{n^{3}}\right]=1 \)