let f and g be functions such that lim g(x) = 2 and lim f(x)/g(x) = π. what is lim f(x)? a π/2 b 2 + π c 2π…

let f and g be functions such that lim g(x) = 2 and lim f(x)/g(x) = π. what is lim f(x)? a π/2 b 2 + π c 2π d the limit cannot be determined from the information given.

let f and g be functions such that lim g(x) = 2 and lim f(x)/g(x) = π. what is lim f(x)? a π/2 b 2 + π c 2π d the limit cannot be determined from the information given.

Answer

Explanation:

Step1: Recall limit - product rule

We know that $\lim_{x\rightarrow a}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow a}f(x)}{\lim_{x\rightarrow a}g(x)}$ (assuming $\lim_{x\rightarrow a}g(x)\neq0$). Given $\lim_{x\rightarrow4}g(x) = 2$ and $\lim_{x\rightarrow4}\frac{f(x)}{g(x)}=\pi$.

Step2: Solve for $\lim_{x\rightarrow4}f(x)$

From $\lim_{x\rightarrow4}\frac{f(x)}{g(x)}=\frac{\lim_{x\rightarrow4}f(x)}{\lim_{x\rightarrow4}g(x)}$, we can cross - multiply. So $\lim_{x\rightarrow4}f(x)=\lim_{x\rightarrow4}\frac{f(x)}{g(x)}\times\lim_{x\rightarrow4}g(x)$. Substitute $\lim_{x\rightarrow4}g(x) = 2$ and $\lim_{x\rightarrow4}\frac{f(x)}{g(x)}=\pi$ into the above formula. Then $\lim_{x\rightarrow4}f(x)=\pi\times2 = 2\pi$.

Answer:

C. $2\pi$