limit and continuity of the sum
Let $f(x)$ and $g(x)$ be two functions, and let $c$ be a real number. The sum of the two functions $f(x)$ and $g(x)$ is defined by $(f+g)(x) = f(x) + g(x)$ for all $x$ in the domain of both functions. To determine if the sum of $f(x)$ and $g(x)$ is continuous at $c$, we need…