I want to calculate
limt→0t2sin2(t)
and I proceed as follows
H=limt→02t2sin(t)cos(t)⟹limt→02tsin(2t)
and when evaluated gives
H=limt→022cos2(t)−2sin2(t)=1
But evaluating the other equivalent term gives
H=limt→022sin(2t)cos(2t)
and that does not exist as the left hand and right hand limits are not equal.
So, what do you think?
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