Worksheets — Set 14

Calculus I · Review and limits

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. Find lim(x→17) (x² − 289)/(x − 17) = ___ 2. If f(x) = 17x³ − 18x, find f′(16) = ___ 3. ∫₀^17 (18x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→16) (x² − 256)/(x − 16) = ___ 2. If f(x) = 16x³ − 17x, find f′(15) = ___ 3. ∫₀^16 (17x + 1) dx = ___ 4. Find critical points of f(x) = x² − 32x + 19 ___ 5. Related rates: radius grows 15 cm/s. Find dV/dt when r = 17. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→19) (x² − 361)/(x − 19) = ___ 8. If f(x) = 19x³ − 20x, find f′(18) = ___

___________________________ ___________________________ ___________________________ ___________________________

More written practice

1. ∫₀^19 (20x + 1) dx = ___ 2. Find critical points of f(x) = x² − 38x + 22 ___ 3. Related rates: radius grows 18 cm/s. Find dV/dt when r = 20. ___ 4. Find lim(x→22) (x² − 484)/(x − 22) = ___ 5. If f(x) = 22x³ − 23x, find f′(21) = ___ 6. ∫₀^22 (23x + 1) dx = ___

___________________________ ___________________________ ___________________________ ___________________________ ___________________________

Patterns and rules

1. Find lim(x→33) (x² − 1089)/(x − 33) = ___ 2. If f(x) = 33x³ − 34x, find f′(32) = ___ 3. ∫₀^33 (34x + 1) dx = ___

_See printable PDF for diagram._

___________________________ ___________________________ ___________________________ ___________________________

Parent tip: Sketch graphs to check signs and behavior