$$\lim_{x \to \infty} \frac{x - 1}{x + 1}$$

$$\lim_{x \to \infty} \frac{x^3 + 2x - 1}{-7x^3 - 4x^2}$$

$$\lim_{x \to 1} \frac{x - 1}{\sqrt{x} - 1}$$

$$\lim_{x \to 0^{+}} \frac{\log{x}}{x}$$

$$\lim_{x \to 0} \frac{\sin{7x}}{x}$$

$$\lim_{x \to 0} \frac{1 - \cos^2{x}}{x^2}$$

$$\lim_{x \to \infty} (1 - \frac{7}{x})^x$$

$$\lim_{x \to \infty} \left(1 + \frac{x}{2}\right)^{\frac{5x + 3}{x}}$$

$$\lim_{x \to \infty} \left( \sqrt{x + 5} - \sqrt{x + 2} \right)$$

$$\lim_{x \to \infty} \left( x - \sqrt{x^2 - 7} \right)$$

$$\lim_{x \to e} \frac{e^x - x^e}{x - e}$$

$$\lim_{x \to 0} \frac{\log(1 + 2x^2)}{x}$$