Worksheets — Set 18

Calculus II · Applications of integration

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

Warm-up

1. Find lim(x→21) (x² − 441)/(x − 21) = ___ 2. If f(x) = 21x³ − 22x, find f′(20) = ___ 3. ∫₀^21 (22x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→20) (x² − 400)/(x − 20) = ___ 2. If f(x) = 20x³ − 21x, find f′(19) = ___ 3. ∫₀^20 (21x + 1) dx = ___ 4. Find critical points of f(x) = x² − 40x + 23 ___ 5. Related rates: radius grows 19 cm/s. Find dV/dt when r = 21. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→23) (x² − 529)/(x − 23) = ___ 8. If f(x) = 23x³ − 24x, find f′(22) = ___

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More written practice

1. ∫₀^23 (24x + 1) dx = ___ 2. Find critical points of f(x) = x² − 46x + 26 ___ 3. Related rates: radius grows 22 cm/s. Find dV/dt when r = 24. ___ 4. Find lim(x→26) (x² − 676)/(x − 26) = ___ 5. If f(x) = 26x³ − 27x, find f′(25) = ___ 6. ∫₀^26 (27x + 1) dx = ___

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Patterns and rules

1. Find lim(x→37) (x² − 1369)/(x − 37) = ___ 2. If f(x) = 37x³ − 38x, find f′(36) = ___ 3. ∫₀^37 (38x + 1) dx = ___

_See printable PDF for diagram._

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Stretch

1. Find lim(x→45) (x² − 2025)/(x − 45) = ___ 2. If f(x) = 45x³ − 46x, find f′(44) = ___

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Parent tip: Sketch graphs to check signs and behavior