Trigonometric Limit without L'hospital (0/0 kind): <munder> <mo form="prefix">lim <mro

Dayanara Terry 2022-07-04 Answered
Trigonometric Limit without L'hospital (0/0 kind): lim x π 6   sin ( x π 6 ) 3 2 cos ( x )
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Answers (1)

sniokd
Answered 2022-07-05 Author has 22 answers
Hint. We have that
lim x π 6   sin ( x π 6 ) 3 2 cos ( x ) = lim t 0 sin ( t ) 3 2 cos ( t + π 6 ) .
Then use the fact that
cos ( t + π 6 ) = cos ( t ) cos ( π 6 ) sin ( t ) sin ( π 6 ) = 3 2 cos ( t ) 1 2 sin ( t ) .
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