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Home » Try n = 10: \( \frac102(10 + 27) = 5 \times 37 = 185 \) - 500apps

Try n = 10: \( \frac102(10 + 27) = 5 \times 37 = 185 \) - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Find the limit \(\lim_{x \to 2} \frac{x^2 - 4}{x - 2}\).

📌 \(\lim_{x \to 2} \frac{(x - 2)(x + 2)}{x - 2} = \lim_{x \to 2} (x + 2)\).

📌 Substitute \(x = 2\): \(2 + 2 = 4\).

📌 If \(\sin(\theta) = \frac{3}{5}\), find \(\cos(\theta)\) for \(0 < \theta < \frac{\pi}{2}\).

📌 Use the identity \(\sin^2(\theta) + \cos^2(\theta) = 1\).

📌 \(\left(\frac{3}{5}\right)^2 + \cos^2(\theta) = 1 \Rightarrow \frac{9}{25} + \cos^2(\theta) = 1\).

📌 \(\cos^2(\theta) = 1 - \frac{9}{25} = \frac{16}{25}\).

📌 \(\cos(\theta) = \frac{4}{5}\) (positive in the first quadrant).

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