Use de moivre's theorem to write [2(cos 12 degrees + i sin 12 degrees)]^5 in standard form
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To check for continuity at the edges of each piece, you need to consider the limit as approaches the edges. For example,
has two pieces, and
, both of which are continuous by themselves on the provided intervals. In order for
to be continuous everywhere, we need to have
By definition of , we have
, and the limits are
The limits match, so is continuous.
For the others: Each of the individual pieces of are continuous functions on their domains, so you just need to check the value of each piece at the edge of each subinterval.