assignment 3: problem 8 (1 point) evaluate the limit $lim_{x\rightarrow0}\frac{\tan x}{4x}=$ you have…

assignment 3: problem 8 (1 point) evaluate the limit $lim_{x\rightarrow0}\frac{\tan x}{4x}=$ you have attempted this problem 0 times. you have unlimited attempts remaining.

assignment 3: problem 8 (1 point) evaluate the limit $lim_{x\rightarrow0}\frac{\tan x}{4x}=$ you have attempted this problem 0 times. you have unlimited attempts remaining.

Answer

Explanation:

Step1: Recall the limit formula

We know that $\lim_{x\rightarrow0}\frac{\tan x}{x}=1$.

Step2: Rewrite the given limit

$\lim_{x\rightarrow0}\frac{\tan x}{4x}=\frac{1}{4}\lim_{x\rightarrow0}\frac{\tan x}{x}$.

Step3: Substitute the known - limit value

Since $\lim_{x\rightarrow0}\frac{\tan x}{x} = 1$, then $\frac{1}{4}\lim_{x\rightarrow0}\frac{\tan x}{x}=\frac{1}{4}\times1$.

Answer:

$\frac{1}{4}$