555

Nice! 555 (lol). Want a quick study boost? Here’s a ready-to-use 5-question calculus mini-quiz with solutions. If you want a different subject, tell me and I’ll tailor it.

Questions:

1. Differentiate f(x) = 3x^4 − 5x^2 + 7.
2. Compute the integral ∫ 2x e^{x^2} dx.
3. Differentiate using the chain rule: d/dx [sin(3x^2)].
4. Evaluate the limit: lim_{x→0} sin(5x)/x.
5. Find the critical points of f(x) = x^3 − 3x^2 + 2x.

Answers (with brief steps):

1. f'(x) = 12x^3 − 10x.
2. Let u = x^2, du = 2x dx. Integral becomes ∫ e^{u} du = e^{u} + C = e^{x^2} + C.
3. d/dx [sin(3x^2)] = cos(3x^2) · (6x) = 6x cos(3x^2).
4. lim_{x→0} sin(5x)/x = 5 (since sin(y) ~ y for small y).
5. f'(x) = 3x^2 − 6x + 2. Set to zero: 3x^2 − 6x + 2 = 0 → x = [6 ± √(36 − 24)]/6 = 1 ± √3/3.

If you want, I can generate a similar mini-quiz for your actual course (subject, topic, and difficulty), or do a longer practice set with solutions.