## Calculus, 10th Edition (Anton)

$$\begin{array}{l}{\text { If } \lim _{x \rightarrow a} f(x) \text { and } \lim _{x \rightarrow a} g(x) \text { exist, then }} \end{array}$$ $$\lim _{x \rightarrow a} f(x)=L_{1} , \lim _{x \rightarrow a} f(x)=L_{2}$$ 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