Examine the continuity of tan(pi/x)

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The discussion focuses on examining the continuity of the function P defined as P(x) = tan(π/x). Participants express confusion regarding the domain of the function, particularly where tan(θ) is not continuous. It is noted that tan(θ) is discontinuous at odd multiples of π/2, which translates to specific values of x that make π/x equal to these points. The conclusion drawn is that P is not continuous at x = 0 and at values corresponding to π/(2k+1) for integers k. Understanding these discontinuities is crucial for analyzing the function's behavior.
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Homework Statement


Examine the continuity of
P: x -----> tan(Pi/x)

2. The attempt at a solution:
I considered fog with f=tan(x) and g=Pi/x
But the problem I have is with the domain of definition
can someone please help !
 
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For what values of \theta is tan(\theta) not continuous? For what values of x is \pi/x= \theta?
 
So P is not continuous on 0 and 2/2k+1 right ??
 

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