Limit \(\displaystyle\lim_{{{x}\to{\frac{{\pi}}{{{3}}}}}}{\frac{{{\sin{{\left({x}-{\frac{{\pi}}{{{3}}}}\right)}}}}}{{{1}-{2}{\cos{{\left\lbrace{x}\right\rbrace}}}}}}\)

Dominique Pace

Dominique Pace

Answered question

2022-03-22

Limit limxπ3sin(xπ3)12cos{x}

Answer & Explanation

Payten Reese

Payten Reese

Beginner2022-03-23Added 10 answers

Set xπ3=t
limt0sint12cos(t+π3)=limt0sint1cost+3sint
=limt02sin(t2)cos(t2)2sin2(t2)+23sin(t2)cos(t2)
=limt0cos(t2)2sin(t2)+3cos(t2)
Now it should be clear. The limit according to me is 13
Kingston Lowery

Kingston Lowery

Beginner2022-03-24Added 10 answers

sin(xπ3)12cosx=sin(xπ3)xπ3xπ312cosx=sinyyy12cos(y+π3)=sinyyy1cosy+3siny13

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