let lim f(x)=5 and lim g(x)=10. 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)=5 and lim g(x)=10. 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.) find the limit. lim f(x)/g(x)= x→9 (simplify your answer.)

let lim f(x)=5 and lim g(x)=10. 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.) find the limit. lim f(x)/g(x)= x→9 (simplify your answer.)

Answer

Explanation:

Step1: Recall quotient - limit rule

The quotient - limit rule states that 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: Apply the rule

Given $\lim_{x\rightarrow9}f(x) = 5$ and $\lim_{x\rightarrow9}g(x)=10$, the expression from applying the rule is $\frac{\lim_{x\rightarrow9}f(x)}{\lim_{x\rightarrow9}g(x)}$.

Step3: Calculate the limit

Substitute the given values: $\frac{\lim_{x\rightarrow9}f(x)}{\lim_{x\rightarrow9}g(x)}=\frac{5}{10}$.

Step4: Simplify the result

$\frac{5}{10}=\frac{1}{2}$.

Answer:

Expression from applying the rule: $\frac{\lim_{x\rightarrow9}f(x)}{\lim_{x\rightarrow9}g(x)}$ Limit: $\frac{1}{2}$