Worksheets — Set 20

Calculus AB · AP · Applications of Integration

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

Warm-up

1. Find lim(x→23) (x² − 529)/(x − 23) = ___ 2. If f(x) = 23x³ − 24x, find f′(22) = ___ 3. ∫₀^23 (24x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→22) (x² − 484)/(x − 22) = ___ 2. If f(x) = 22x³ − 23x, find f′(21) = ___ 3. ∫₀^22 (23x + 1) dx = ___ 4. Find critical points of f(x) = x² − 44x + 25 ___ 5. Related rates: radius grows 21 cm/s. Find dV/dt when r = 23. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→25) (x² − 625)/(x − 25) = ___ 8. If f(x) = 25x³ − 26x, find f′(24) = ___

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More written practice

1. ∫₀^25 (26x + 1) dx = ___ 2. Find critical points of f(x) = x² − 50x + 28 ___ 3. Related rates: radius grows 24 cm/s. Find dV/dt when r = 26. ___ 4. Find lim(x→28) (x² − 784)/(x − 28) = ___ 5. If f(x) = 28x³ − 29x, find f′(27) = ___ 6. ∫₀^28 (29x + 1) dx = ___

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Patterns and rules

1. Find lim(x→39) (x² − 1521)/(x − 39) = ___ 2. If f(x) = 39x³ − 40x, find f′(38) = ___ 3. ∫₀^39 (40x + 1) dx = ___

_See printable PDF for diagram._

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Stretch

1. Find lim(x→47) (x² − 2209)/(x − 47) = ___ 2. If f(x) = 47x³ − 48x, find f′(46) = ___

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Parent tip: Sketch graphs to check signs and behavior