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Calculus Level 4

Given that \( f(x) \) satisfy the equation \[ \displaystyle \int f(x) \, dx = x f(x) + \dfrac{e^{-x^2}}{\sqrt \pi} + C, \] where \(C\) is the constant of integration.

If we know that \(f(0) = 0\) and \( \displaystyle \lim_{n\to\infty} f(n) = 1\), compute \(f'(0) \) to 2 decimal places.

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