Is tan x continuous?
Understand the Problem
The question is asking whether the tangent function, denoted as tan(x), is continuous over its domain. To determine this, we will consider the points at which the tangent function is defined and analyze its behavior around those points.
Answer
tan(x) is continuous everywhere except at (2n+1)π/2.
The final answer is tan(x) is continuous everywhere except at the points (2n+1)π/2, where n ∈ Z.
Answer for screen readers
The final answer is tan(x) is continuous everywhere except at the points (2n+1)π/2, where n ∈ Z.
More Information
The tangent function is discontinuous at (2n+1)π/2 because it approaches infinity or negative infinity, leading to an undefined behavior.
Tips
A common mistake is to assume tan(x) is continuous at all points without considering the domain restrictions where cos(x) = 0.
Sources
- Why is tanx not a continuous function? - Mathematics Stack Exchange - math.stackexchange.com
- Is tan(x) a continous function? - Quora - quora.com
- Prove that the function defined by fx = tan x is a continuous function. - byjus.com
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