Worksheets — Set 6

Calculus BC · AP · Infinite Sequences and Series

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

Warm-up

1. Find lim(x→9) (x² − 81)/(x − 9) = ___ 2. If f(x) = 9x³ − 10x, find f′(8) = ___ 3. ∫₀^9 (10x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→8) (x² − 64)/(x − 8) = ___ 2. If f(x) = 8x³ − 9x, find f′(7) = ___ 3. ∫₀^8 (9x + 1) dx = ___ 4. Find critical points of f(x) = x² − 16x + 11 ___ 5. Related rates: radius grows 7 cm/s. Find dV/dt when r = 9. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→11) (x² − 121)/(x − 11) = ___ 8. If f(x) = 11x³ − 12x, find f′(10) = ___

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More written practice

1. ∫₀^11 (12x + 1) dx = ___ 2. Find critical points of f(x) = x² − 22x + 14 ___ 3. Related rates: radius grows 10 cm/s. Find dV/dt when r = 12. ___ 4. Find lim(x→14) (x² − 196)/(x − 14) = ___ 5. If f(x) = 14x³ − 15x, find f′(13) = ___ 6. ∫₀^14 (15x + 1) dx = ___

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Patterns and rules

1. Find lim(x→25) (x² − 625)/(x − 25) = ___ 2. If f(x) = 25x³ − 26x, find f′(24) = ___ 3. ∫₀^25 (26x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior