if lim g(x) = -6, what is the value of lim xg(x)? x→0 x→0

Answer:

0

Explanation:

Step1: Recall limit - product rule

$\lim_{x\rightarrow a}[f(x)g(x)]=\lim_{x\rightarrow a}f(x)\cdot\lim_{x\rightarrow a}g(x)$ Here $f(x) = x$ and $g(x)$ is given, and $a = 0$.

Step2: Find $\lim_{x\rightarrow0}x$

$\lim_{x\rightarrow0}x=0$

Step3: Find $\lim_{x\rightarrow0}[xg(x)]$

$\lim_{x\rightarrow0}[xg(x)]=\lim_{x\rightarrow0}x\cdot\lim_{x\rightarrow0}g(x)$ Since $\lim_{x\rightarrow0}x = 0$ and $\lim_{x\rightarrow0}g(x)=-6$, then $\lim_{x\rightarrow0}[xg(x)]=0\times(-6)=0$.