if $lim_{x\rightarrow - 8}g(x)=3$, what is the value of $lim_{x\rightarrow - 8}13g(x)$?
if $lim_{x\rightarrow - 8}g(x)=3$, what is the value of $lim_{x\rightarrow - 8}13g(x)$?
Answer
Explanation:
Step1: Apply limit - constant multiple rule
The limit - constant multiple rule states that $\lim_{x\rightarrow a}[cf(x)] = c\lim_{x\rightarrow a}f(x)$, where $c$ is a constant. Here, $c = 13$ and $f(x)=g(x)$ and $a=-8$. So, $\lim_{x\rightarrow - 8}[13g(x)]=13\lim_{x\rightarrow - 8}g(x)$.
Step2: Substitute the given limit value
We know that $\lim_{x\rightarrow - 8}g(x) = 3$. Substituting this value into the expression $13\lim_{x\rightarrow - 8}g(x)$, we get $13\times3$. $13\times3 = 39$.
Answer:
39