4

Not sure what you mean by "4". Do you want a 4-question practice set, four topics to review, or something else? Tell me the subject and level (e.g., Calculus I, Linear Algebra, Statistics, Physics). If you’d like, I can generate a 4-question mini-quiz with solutions right away.

Here’s a ready-to-use 4-question mini-quiz in Calculus I to try (with solutions):

1. Differentiate f(x) = x^3 sin x.

• Answer: f'(x) = 3x^2 sin x + x^3 cos x (product rule).

2. Evaluate the limit: lim_{x→0} (sin x)/x.

• Answer: 1.

3. Maximize A = x^2 y subject to x + y = 10 and x, y ≥ 0.

• Approach: y = 10 − x, so A(x) = x^2(10 − x).
• Critical points: A'(x) = 20x − 3x^2 = x(20 − 3x) ⇒ x = 0 or x = 20/3.
• Positive interior solution: x = 20/3, y = 10 − 20/3 = 10/3.
• Maximum value: A = (20/3)^2(10/3) = 4000/27 ≈ 148.15.

4. Solve the differential equation dy/dx = x + y with initial condition y(0) = 2.

• Solution: y(x) = −x − 1 + 3e^{x}.

If you want a different subject or a longer 4-question set, tell me the topic and level and I’ll tailor it.