limit \lim_{t \to 0}\frac{\sin 3t}{\tan2t} I am struggling with this question.

Judith Warner 2022-04-29 Answered
limit limt0sin3ttan2t
I am struggling with this question. I have attempted it, but I keep getting stuck on the following step:
limt012sin3tcos2tsintcost
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Answers (2)

Larry Hogan
Answered 2022-04-30 Author has 20 answers
You started correctly. Now multiply both numerator and denominator by corresponding ts to get:
L=limt0sin{3t}3t2tsin{2t}32cos{2t}=11321=32.
Note: It was used the remarkable limit: limx0sin{x}x=limx0xsin{x}=1
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hadnya1qd
Answered 2022-05-01 Author has 15 answers
I suspect the denominateur is tan2t. If I'm right, just use equivalents: near 0, we have
sinu~0u,tanu~0u
so that
sin3xtan2x~03x2x=32
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