e 2\). Simplify and find \(\lim_{x o 2} f(x)\).
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- Evaluate the integral \(\int_0^1 (3x^2 + 2x) \, dx\).
- 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
- 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 \(x = 1\).
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