Question

If $\underset{x\to a}{lim}$[f(x) + g(x)] = 10 and $\underset{x\to a}{lim}$ f(x)=2, then find the value of $\underset{x\to a}{lim}$ g(x), provided the limit

exist

Answer 1

If the limits $\underset{x\to a}{lim}$ f(x) and $\underset{x\to a}{lim}$ g(x) exist, then $\underset{x\to a}{lim}$ [f(x)+g(x)] = $\underset{x\to a}{lim}$ f(x) + $\underset{x\to a}{lim}$ g(x)

$\Rightarrow$ 10 = 2+ $\underset{x\to a}{lim}$ g(x)

$\Rightarrow$ $\underset{x\to a}{lim}$ g(x) = 8