Basic Limit Properties

Assuming $$\lim_{x \to a} f(x)$$ and $$\lim_{x \to a} g(x)$$ exist:

• Sum: $$\lim_{x \to a} [f(x) + g(x)] = \lim_{x \to a} f(x) + \lim_{x \to a} g(x)$$
• Product: $$\lim_{x \to a} [f(x) \cdot g(x)] = \lim_{x \to a} f(x) \cdot \lim_{x \to a} g(x)$$
• Quotient: $$\lim_{x \to a} \frac{f(x)}{g(x)} = \frac{\lim_{x \to a} f(x)}{\lim_{x \to a} g(x)}$$ (if $$\lim_{x \to a} g(x) \neq 0$$)