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Home » \[ FV = 1000 \times (1 + 0.05)^10 = 1000 \times 1.62889 \approx 1628.89 \] - go-checkin.com

\[ FV = 1000 \times (1 + 0.05)^10 = 1000 \times 1.62889 \approx 1628.89 \] - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Let $ y = \sin^2 x $, where $ y > 0 $. Then:

📌 g(x) = 2y + 2 + \frac{1}{2y}

📌 We minimize $ 2y + \frac{1}{2y} + 2 $. Let:

📌 h(y) = 2y + \frac{1}{2y}

📌 Using the AM-GM inequality:

📌 2y + \frac{1}{2y} \geq 2\sqrt{2y \cdot \frac{1}{2y}} = 2

📌 Equality holds when $ 2y = \frac{1}{2y} \Rightarrow 4y^2 = 1 \Rightarrow y = \frac{1}{2} $.

📌 g(x) = h(y) + 2 = 2 + 2 = 4

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