{"conversations": [{"from": "human", "value": "Lagun diezadakezu Big O notazioa erakusten LaTeX-en? $T(n) ={15n}^3+n^2+4$-ek frogatzen du $T(n)=n^3)=O(n^3)$. Sindukzio formal bat nahi nuke, $c$ eta $n_0$ baliodun bat erabiltzen dituena."}, {"from": "gpt", "value": "$T(n)={15n}^3+n+4 \\\\ {15n}^3+n^2+4 \\le {15n}^3+n+n^3+{4n}^3^3, orduan: \\t; x>1\\\\ {15n}^3+n+4} \\le {20n}^3 \\\\y; c=20, n0=1=$"}, {"from": "human", "value": "Eskerrik asko erantzuteagatik."}, {"from": "gpt", "value": "Beste zerbaitekin laguntzerik badut, esadazu."}]}