Chapter 14.3, Problem 68AYU

To determine

To find: The numbers at which $f$ is continuous.

Answer to Problem 68AYU

Continuous for all real values of $x$ excluding $x=0$.

Explanation of Solution

Given:

$f\left(x\right)=4\text{csc}x$

Calculation:

$f\left(x\right)=4\text{csc}x$ is a trigonometric function.

Since $\text{csc}x=\frac{1}{\text{sin}x}$ is undefined for $x=0$; therefore $f\left(x\right)=4\text{csc}x$ is continuous for all real numbers excluding $x=0$.