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Home » e 2\). Simplify and find \(\lim_x o 2 f(x)\). - Appcentric

e 2\). Simplify and find \(\lim_x o 2 f(x)\). - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 A_{ ext{sector}} = rac{1}{2} r^2 heta = rac{1}{2} \cdot 16 \cdot rac{2\pi}{3} = rac{16\pi}{3}

📌 Area of triangle \(OAB\):

📌 A_{ ext{triangle}} = rac{1}{2} ab \sin heta = rac{1}{2} (2\sqrt{6})(2\sqrt{6}) \sin\left(rac{2\pi}{3}

📌 ight) = rac{1}{2} \cdot 24 \cdot rac{\sqrt{3}}{2} = 6\sqrt{3}

📌 Area of segment (the smaller region bounded by the chord and arc) is:

📌 A = A_{ ext{sector}} - A_{ ext{triangle}} = rac{16\pi}{3} - 6\sqrt{3}

📌 But since the line \(y = x + 2\) cuts the circle from top-right to bottom-left, the region enclosed is actually the smaller segment. Hence, the area is:

📌 oxed{rac{16\pi}{3} - 6\sqrt{3}}

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