Review — Difficulty 8/10
Calculus III · Partial derivatives and optimization
Review skills for this standard. Write answers where shown.
Together with a parent
1. Find lim(x→13) (x² − 169)/(x − 13) = ___ 2. If f(x) = 13x³ − 14x, find f′(12) = ___ 3. ∫₀^13 (14x + 1) dx = ___
Written review
1. Find lim(x→15) (x² − 225)/(x − 15) = ___ 2. If f(x) = 15x³ − 16x, find f′(14) = ___ 3. ∫₀^15 (16x + 1) dx = ___ 4. Find critical points of f(x) = x² − 30x + 18 ___ 5. Related rates: radius grows 14 cm/s. Find dV/dt when r = 16. ___ 6. State the meaning of f′(a) in context. ___
_See printable PDF for diagram._
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Skills checklist
- [ ] Computes limits and derivatives accurately
- [ ] Sets up and evaluates definite integrals
- [ ] Explains results in applied settings
- [ ] Explains Partial derivatives and optimization without prompts
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