Worksheets — Set 13

Calculus I · Review and limits

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

Warm-up

1. Find lim(x→16) (x² − 256)/(x − 16) = ___ 2. If f(x) = 16x³ − 17x, find f′(15) = ___ 3. ∫₀^16 (17x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→15) (x² − 225)/(x − 15) = ___ 2. If f(x) = 15x³ − 16x, find f′(14) = ___ 3. ∫₀^15 (16x + 1) dx = ___ 4. Find critical points of f(x) = x² − 30x + 18 ___ 5. Related rates: radius grows 14 cm/s. Find dV/dt when r = 16. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→18) (x² − 324)/(x − 18) = ___ 8. If f(x) = 18x³ − 19x, find f′(17) = ___

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More written practice

1. ∫₀^18 (19x + 1) dx = ___ 2. Find critical points of f(x) = x² − 36x + 21 ___ 3. Related rates: radius grows 17 cm/s. Find dV/dt when r = 19. ___ 4. Find lim(x→21) (x² − 441)/(x − 21) = ___ 5. If f(x) = 21x³ − 22x, find f′(20) = ___ 6. ∫₀^21 (22x + 1) dx = ___

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Patterns and rules

1. Find lim(x→32) (x² − 1024)/(x − 32) = ___ 2. If f(x) = 32x³ − 33x, find f′(31) = ___ 3. ∫₀^32 (33x + 1) dx = ___

_See printable PDF for diagram._

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Parent tip: Sketch graphs to check signs and behavior