Find the derivative of the function \( f(x) = 3x^2 + 5x - 8 \).
Solution: The derivative is \( f'(x) = 6x + 5 \).
Evaluate the integral \(\int (2x^3 - x + 1) \, dx\).
Solution: The integral is \( \frac{1}{2}x^4 - \frac{1}{2}x^2 + x + C \), where C is the constant of integration.
Calculate the limit: \(\lim_{{x \to 2}} \frac{x^2 - 4}{x - 2}\).
Solution: Simplifying, we find \(\lim_{{x \to 2}} (x + 2) = 4\).
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