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

Dayanara Terry

Dayanara Terry

Answered question

2022-07-04

Trigonometric Limit without L'hospital (0/0 kind): lim x π 6   sin ( x π 6 ) 3 2 cos ( x )

Answer & Explanation

sniokd

sniokd

Beginner2022-07-05Added 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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