Question

Calculati stiind ca exista urmatoarea limita, fara a folosi notiunea de derivata.

Answer 1

Foloseste-te de formula: $\lim_{x \to \00} \frac{sin(x)}{x} = 1$
mai intai imparti limita in doua:

$\lim_{x \to \00} \frac{sin(x)}{ x^{3} } - \lim_{x \to \00} \frac{x}{ x^{3} } = \lim_{x \to \00} \frac{sin(x)}{ x } * \frac{x}{x^{3}} - \lim_{x \to \00} \frac{x}{ x^{3} }$
=$lim_{x \to \00} \frac{x}{x^{3}} - \lim_{x \to \00} \frac{x}{ x^{3} }$ = 0

Poti face asta si fara sa o imparti in doua limite, presupun ca asa ar fi mai simplu.