Worksheets — Set 1

Calculus II · Integration techniques

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

Warm-up

1. Find lim(x→4) (x² − 16)/(x − 4) = ___ 2. If f(x) = 4x³ − 5x, find f′(3) = ___ 3. ∫₀^4 (5x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→3) (x² − 9)/(x − 3) = ___ 2. If f(x) = 3x³ − 4x, find f′(2) = ___ 3. ∫₀^3 (4x + 1) dx = ___ 4. Find critical points of f(x) = x² − 6x + 6 ___ 5. Related rates: radius grows 2 cm/s. Find dV/dt when r = 4. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→6) (x² − 36)/(x − 6) = ___ 8. If f(x) = 6x³ − 7x, find f′(5) = ___

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More written practice

1. ∫₀^6 (7x + 1) dx = ___ 2. Find critical points of f(x) = x² − 12x + 9 ___ 3. Related rates: radius grows 5 cm/s. Find dV/dt when r = 7. ___ 4. Find lim(x→9) (x² − 81)/(x − 9) = ___ 5. If f(x) = 9x³ − 10x, find f′(8) = ___ 6. ∫₀^9 (10x + 1) dx = ___

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Patterns and rules

1. Find lim(x→20) (x² − 400)/(x − 20) = ___ 2. If f(x) = 20x³ − 21x, find f′(19) = ___ 3. ∫₀^20 (21x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior