Answer
The statement is true
Work Step by Step
$$
\begin{array}{l}{\text { If } \lim _{x \rightarrow a} f(x) \text { and } \lim _{x \rightarrow a} g(x) \text { exist, then }} \end{array}
$$
$$
\lim _{x \rightarrow a} f(x)=L_{1} , \lim _{x \rightarrow a} f(x)=L_{2}
$$
where $L_{1} , L_{2}$ are constant
by Theorem 1.2.2(a) we have
$$
\lim _{x \rightarrow a}[f(x)+g(x)]=\lim _{x \rightarrow a} f(x)+\lim _{x \rightarrow a} g(x)=L_{1}+L_{2}
$$
Thus
$$
\lim _{x \rightarrow a}[f(x)+g(x)]=L_{1}+L_{2}=L_{3}
$$
then $$
\lim _{x \rightarrow a}[f(x)+g(x)]
$$
Therefore the statement is true
