Calculus Examples

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

Step 1

Since $\frac{x^{2} \cdot 2}{x + 100} \leq \frac{x^{2} (2 + \sin^{2} (x))}{x + 100} \leq \frac{x^{2} \cdot 3}{x + 100}$ and $lim_{x \to \infty} \frac{x^{2} \cdot 2}{x + 100} = lim_{x \to \infty} \frac{x^{2} \cdot 3}{x + 100} = \infty$ , apply the squeeze theorem.

$\infty$