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Home » The quotient is \( x^2 - 5x + 6 \), so: - Abu Waleed Tea

The quotient is \( x^2 - 5x + 6 \), so: - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Integrate term by term: \(\int 3x^2 dx = x^3\), \(\int 2x dx = x^2\), so \(\int_0^1 (3x^2 + 2x) dx = [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2\).

📌 A function \(f(x) = rac{x^2 - 4}{x - 2}\) is defined for \(x

📌 e 2\). Simplify and find \(\lim_{x o 2} f(x)\).

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

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