if lim f(x) = 2 and lim g(x) = 0, what is the value of lim g(x) + f(x)? x→-2 x→-2 x→-2

Answer:

2

Explanation:

Step1: Recall limit - sum rule

$\lim_{x\rightarrow a}[f(x)+g(x)]=\lim_{x\rightarrow a}f(x)+\lim_{x\rightarrow a}g(x)$

Step2: Substitute given values

$\lim_{x\rightarrow - 2}[f(x)+g(x)]=\lim_{x\rightarrow - 2}f(x)+\lim_{x\rightarrow - 2}g(x)$ Since $\lim_{x\rightarrow - 2}f(x) = 2$ and $\lim_{x\rightarrow - 2}g(x)=0$, then $\lim_{x\rightarrow - 2}[f(x)+g(x)]=2 + 0=2$.