Proving limit laws

\(\displaystyle \lim_{x \to c} [f(x) + g(x)] = \lim_{x \to c} f(x) + \lim_{x \to c} g(x)\)
\(\displaystyle \lim_{x \to c} b \cdot f(x) = b \cdot \lim_{x \to c} f(x)\)