Is tan(x) continuous?
Understand the Problem
The question is asking whether the tangent function, denoted as tan(x), is a continuous function across its domain. To answer this, we will consider the properties of the tangent function and identify any points of discontinuity.
Answer
tan(x) is continuous except at points x = kπ/2, where k is an odd integer.
The final answer is tan(x) is continuous except at points x = kπ/2, where k is an odd integer.
Answer for screen readers
The final answer is tan(x) is continuous except at points x = kπ/2, where k is an odd integer.
More Information
Continuity of a function means that the function has no breaks, jumps, or holes in its graph. The points where tan(x) is discontinuous correspond to the values of x where cos(x) is zero, as tan(x) = sin(x) / cos(x). At those points, the function is undefined and therefore discontinuous.
Tips
A common mistake is to assume tan(x) is continuous over all real numbers. Remember, it is not defined and thus not continuous at x = kπ/2, for k as an odd integer.
Sources
- Why is tanx not a continuous function? - Mathematics Stack Exchange - math.stackexchange.com
- Does tan(x) considered continuous or discontinuous? - Reddit - reddit.com
