Define the function
p(x)=∣x−π∣tanx,0<x<2π,x=π.
(a) List all real numbers in (0,2π) at which p is not defined and explain why each number lies outside the domain.
(b) For each point identified in part (a), evaluate one-sided limits of p(x) as x approaches that point, showing all analytic work.
(c) Determine every open subinterval of (0,2π) on which p is continuous. Express your answer in interval notation and justify it with reference to your limit calculations and properties of continuous functions.
(d) Sketch a qualitative graph of p on its domain, labeling all vertical asymptotes and indicating the behavior near each discontinuity you found.