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Home » Divide \( -v^2 \) by \( v^2 \), giving \(-1\). - Ready Digital AB

Divide \( -v^2 \) by \( v^2 \), giving \(-1\). - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Factor numerator: \(x^2 - 4 = (x - 2)(x + 2)\), so \(f(x) = rac{(x - 2)(x + 2)}{x - 2} = x + 2\) for \(x

📌 Thus, \(\lim_{x o 2} f(x) = 2 + 2 = 4\).

📌 Find the derivative of \(f(x) = \ln(x^2 + 1)\) at \(x = 1\).

📌 Use chain rule: \(f'(x) = rac{1}{x^2 + 1} \cdot 2x = rac{2x}{x^2 + 1}\).

📌 At \(x = 1\): \(f'(1) = rac{2(1)}{1 + 1} = rac{2}{2} = 1\).

📌 The sum of the first \(n\) terms of an arithmetic sequence is \(S_n = 3n^2 + 5n\). Find the 10th term.

📌 The \(n\)th term is \(a_n = S_n - S_{n-1}\).

📌 Compute \(S_{10} = 3(10)^2 + 5(10) = 300 + 50 = 350\).

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