let lim f(x)=2 and lim g(x)=6. use the limit rules to find the limit below. x→9 x→9 lim f(x)/g(x) x→9 what…

let lim f(x)=2 and lim g(x)=6. use the limit rules to find the limit below. x→9 x→9 lim f(x)/g(x) x→9 what expression results from applying the appropriate limit rule? (do not simplify.)

let lim f(x)=2 and lim g(x)=6. use the limit rules to find the limit below. x→9 x→9 lim f(x)/g(x) x→9 what expression results from applying the appropriate limit rule? (do not simplify.)

Answer

Explanation:

Step1: Recall quotient - limit rule

If $\lim_{x\rightarrow a}f(x) = L$ and $\lim_{x\rightarrow a}g(x)=M$ ($M\neq0$), then $\lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow a}f(x)}{\lim_{x\rightarrow a}g(x)}$.

Step2: Substitute given limits

Given $\lim_{x\rightarrow9}f(x) = 2$ and $\lim_{x\rightarrow9}g(x)=6$, we substitute into the quotient - limit rule formula. The expression is $\frac{\lim_{x\rightarrow9}f(x)}{\lim_{x\rightarrow9}g(x)}$

Answer:

$\frac{\lim_{x\rightarrow9}f(x)}{\lim_{x\rightarrow9}g(x)}$