#Removing Discontinuity | Trig piecewise functions

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rare plover
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I guess I comprehend on how to solve it... but how are these two alike?? (9-10 vs 11-12)

How do I visualize and understand 11 and 12? I guess I know how the process works to solve it, but don't understand the whole picture, the "why."

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vestal bearBOT