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Here are four quick calculus-style practice questions (with solutions). If you want a different subject, just tell me.

1. Limit Compute lim_{x→0} (sin x) / x. Solution: This standard limit equals 1. (Alternative: use L’Hôpital’s rule or the squeeze theorem.)

2. Derivative Differentiate f(x) = x^3 e^{2x}. Solution: f'(x) = e^{2x}(3x^2 + 2x^3).

3. Integral Evaluate ∫_0^1 x e^x dx. Solution: Use integration by parts with u = x, dv = e^x dx. ∫_0^1 x e^x dx = [x e^x]_0^1 − ∫_0^1 e^x dx = (1·e) − (e − 1) = 1.

4. Sequence/Limit Find lim_{n→∞} (1 + 1/n)^n. Solution: The limit is e (the sequence converges to e).

If you’d like, I can tailor these to a specific subject (e.g., linear algebra, statistics, physics) or adjust difficulty. How would you like to proceed?