Worksheets — Set 17

Business calculus · Differentiation and applications

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

Warm-up

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._

Written practice

1. Find lim(x→19) (x² − 361)/(x − 19) = ___ 2. If f(x) = 19x³ − 20x, find f′(18) = ___ 3. ∫₀^19 (20x + 1) dx = ___ 4. Find critical points of f(x) = x² − 38x + 22 ___ 5. Related rates: radius grows 18 cm/s. Find dV/dt when r = 20. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→22) (x² − 484)/(x − 22) = ___ 8. If f(x) = 22x³ − 23x, find f′(21) = ___

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More written practice

1. ∫₀^22 (23x + 1) dx = ___ 2. Find critical points of f(x) = x² − 44x + 25 ___ 3. Related rates: radius grows 21 cm/s. Find dV/dt when r = 23. ___ 4. Find lim(x→25) (x² − 625)/(x − 25) = ___ 5. If f(x) = 25x³ − 26x, find f′(24) = ___ 6. ∫₀^25 (26x + 1) dx = ___

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Patterns and rules

1. Find lim(x→36) (x² − 1296)/(x − 36) = ___ 2. If f(x) = 36x³ − 37x, find f′(35) = ___ 3. ∫₀^36 (37x + 1) dx = ___

_See printable PDF for diagram._

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Stretch

1. Find lim(x→44) (x² − 1936)/(x − 44) = ___ 2. If f(x) = 44x³ − 45x, find f′(43) = ___

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Parent tip: Sketch graphs to check signs and behavior