Calculating lim x → π 6 ( sin ⁡ ( x − π 6 )...

hryggcx

hryggcx

Answered

2022-06-29

Calculating lim x π 6 ( sin ( x π 6 ) 3 2 cos x ) , without using L'Hospital rule

Answer & Explanation

Perman7z

Perman7z

Expert

2022-06-30Added 13 answers

Let put t = x π 6
we will compute
lim t 0 sin ( t ) 3 2 cos ( t + π 6 ) =
lim t 0 sin ( t ) 3 2 ( 1 cos ( t ) ) + sin ( t ) 2 =
lim t 0 1 1 2 + 3 2 t 2 ( 1 cos ( t ) ) t 2 sin ( t ) = 2.

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