Chapter 14.3, Problem 67AYU

To determine

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

Answer to Problem 67AYU

Continuous for all real values of $x$ excluding $x=\pm \frac{\pi }{2}$.

Explanation of Solution

Given:

$f\left(x\right)=2\text{tan}x$

Calculation:

$f\left(x\right)=2\text{tan}x$ is a trigonometric function.

Since $\text{tan}x=\frac{\text{sin}x}{\text{cos}x}$ is undefined for $x=\pm \frac{\pi }{2}$; therefore $f\left(x\right)=2\text{tan}x$ is continuous for all real numbers excluding $x=\pm \frac{\pi }{2}$.