2. $$ \lim _{x \rightarrow \infty} \frac{x^{2}}{5-x^{3}} $$

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Calculate the limit $$ \lim _{x ightarrow \infty} \frac{x^{2}}{5-x^{3}} $$.
Evaluate the limit by following steps:
- step0: Evaluate using transformations:
  $$\lim _{xightarrow +\infty}\left(\frac{x^{2}}{5-x^{3}}ight)$$
- step1: Rewrite the expression:
  $$\lim _{xightarrow +\infty}\left(\frac{x^{2}}{x^{3}}	imes \frac{1}{\frac{5}{x^{3}}-1}ight)$$
- step2: Calculate:
  $$\lim _{xightarrow +\infty}\left(\frac{1}{x}	imes \frac{1}{\frac{5}{x^{3}}-1}ight)$$
- step3: Rewrite the expression:
  $$\lim _{xightarrow +\infty}\left(\frac{1}{x}ight)	imes \lim _{xightarrow +\infty}\left(\frac{1}{\frac{5}{x^{3}}-1}ight)$$
- step4: Calculate:
  $$\lim _{xightarrow +\infty}\left(\frac{1}{x}ight)	imes \frac{\lim _{xightarrow +\infty}\left(1ight)}{\lim _{xightarrow +\infty}\left(\frac{5}{x^{3}}-1ight)}$$
- step5: Rewrite the expression:
  $$\lim _{xightarrow +\infty}\left(\frac{1}{x}ight)	imes \frac{1}{\lim _{xightarrow +\infty}\left(\frac{5}{x^{3}}-1ight)}$$
- step6: Rewrite the expression:
  $$\lim _{xightarrow +\infty}\left(\frac{1}{x}ight)	imes \frac{1}{-1}$$
- step7: Rewrite the expression:
  $$0	imes \frac{1}{-1}$$
- step8: Calculate:
  $$0	imes \left(-1ight)$$
- step9: Calculate:
  $$0$$
La limita de $$ \frac{x^{2}}{5-x^{3}} $$ cuando $$ x $$ tiende a infinito es 0.
La limita es 0.

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