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$lim_{x \to \infty} \frac{x^{2} (2 + \sin^{2} (x))}{x + 100}$

Langkah 1

Karena $\frac{x^{2} \cdot 2}{x + 100} \leq \frac{x^{2} (2 + \sin^{2} (x))}{x + 100} \leq \frac{x^{2} \cdot 3}{x + 100}$ dan $lim_{x \to \infty} \frac{x^{2} \cdot 2}{x + 100} = lim_{x \to \infty} \frac{x^{2} \cdot 3}{x + 100} = \infty$ , terapkan Teorema Apit.

$\infty$