Question

at what points is the function y = $\frac{cos x}{6x}$ continuous?
describe the set of x - values where the function is continuous, using interval notation
(simplify your answer. type your answer in interval notation.)

Explanation:

Step1: Recall continuity condition

A rational - function $\frac{f(x)}{g(x)}$ is continuous everywhere except where $g(x)=0$. Here, $f(x)=\cos x$ and $g(x) = 6x$.

Step2: Find the discontinuous point

Set $g(x)=0$. So, $6x = 0$, which gives $x = 0$.

Step3: Write the continuous intervals

The function $y=\frac{\cos x}{6x}$ is continuous for all real numbers except $x = 0$. In interval notation, the set of continuous $x$ - values is $(-\infty,0)\cup(0,\infty)$.

Answer:

$(-\infty,0)\cup(0,\infty)$