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doubletree suites by hilton hotel raleigh durham durham nc - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Derivative:

📌 \[ f'(x) = 12x^2 - 10x + 2 \]

📌 If a geometric sequence has a first term of 5 and a common ratio of 3, what is the 4th term?

📌 The \(n\)-th term of a geometric sequence is given by \(a_n = a \cdot r^{n-1}\).

📌 Substitute \(a = 5\), \(r = 3\), and \(n = 4\):

📌 \[ a_4 = 5 \cdot 3^{4-1} = 5 \cdot 3^3 = 5 \cdot 27 = 135 \]

📌 Evaluate the integral \(\int (2x^2 + 3x + 1) \, dx\).

📌 \[ \int 2x^2 \, dx = rac{2}{3}x^3, \quad \int 3x \, dx = rac{3}{2}x^2, \quad \int 1 \, dx = x \]

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