Worksheets — Set 3

Calculus II · Introductory differential equations

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

Warm-up

1. Find lim(x→6) (x² − 36)/(x − 6) = ___ 2. If f(x) = 6x³ − 7x, find f′(5) = ___ 3. ∫₀^6 (7x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→5) (x² − 25)/(x − 5) = ___ 2. If f(x) = 5x³ − 6x, find f′(4) = ___ 3. ∫₀^5 (6x + 1) dx = ___ 4. Find critical points of f(x) = x² − 10x + 8 ___ 5. Related rates: radius grows 4 cm/s. Find dV/dt when r = 6. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→8) (x² − 64)/(x − 8) = ___ 8. If f(x) = 8x³ − 9x, find f′(7) = ___

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More written practice

1. ∫₀^8 (9x + 1) dx = ___ 2. Find critical points of f(x) = x² − 16x + 11 ___ 3. Related rates: radius grows 7 cm/s. Find dV/dt when r = 9. ___ 4. Find lim(x→11) (x² − 121)/(x − 11) = ___ 5. If f(x) = 11x³ − 12x, find f′(10) = ___ 6. ∫₀^11 (12x + 1) dx = ___

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Patterns and rules

1. Find lim(x→22) (x² − 484)/(x − 22) = ___ 2. If f(x) = 22x³ − 23x, find f′(21) = ___ 3. ∫₀^22 (23x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior