determine for what numbers, if any, the given function is discontinuous. f(x)=sin 13x/x select the correct…
determine for what numbers, if any, the given function is discontinuous. f(x)=sin 13x/x select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the function is discontinuous at (use a comma to separate answers as needed.) b. the function is continuous everywhere.
Answer
Explanation:
Step1: Recall continuity condition
A function $y = f(x)$ is discontinuous at $x = a$ if $f(a)$ is not defined. For the function $f(x)=\frac{\sin 13x}{x}$, when $x = 0$, the function has the form $\frac{0}{0}$.
Step2: Analyze domain - related discontinuity
The function $f(x)=\frac{\sin 13x}{x}$ is not defined at $x = 0$ because division by zero is undefined in the real - number system.
Answer:
A. The function is discontinuous at $0$