if lim g(x) = -2, what is the value of lim xg(x)? x→10 x→10

Answer:

-20

Explanation:

Step1: Apply 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 $a = 10$.

Step2: Find $\lim_{x\rightarrow10}x$

$\lim_{x\rightarrow10}x=10$

Step3: Find $\lim_{x\rightarrow10}[xg(x)]$

$\lim_{x\rightarrow10}[xg(x)]=\lim_{x\rightarrow10}x\cdot\lim_{x\rightarrow10}g(x)$ Since $\lim_{x\rightarrow10}x = 10$ and $\lim_{x\rightarrow10}g(x)=-2$, then $\lim_{x\rightarrow10}[xg(x)]=10\times(-2)=-20$