Worksheets — Set 16

Business calculus · Integration and multivariable basics

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

Warm-up

1. Find lim(x→19) (x² − 361)/(x − 19) = ___ 2. If f(x) = 19x³ − 20x, find f′(18) = ___ 3. ∫₀^19 (20x + 1) dx = ___

_See printable PDF for diagram._

Written practice

1. Find lim(x→18) (x² − 324)/(x − 18) = ___ 2. If f(x) = 18x³ − 19x, find f′(17) = ___ 3. ∫₀^18 (19x + 1) dx = ___ 4. Find critical points of f(x) = x² − 36x + 21 ___ 5. Related rates: radius grows 17 cm/s. Find dV/dt when r = 19. ___ 6. State the meaning of f′(a) in context. ___ 7. Find lim(x→21) (x² − 441)/(x − 21) = ___ 8. If f(x) = 21x³ − 22x, find f′(20) = ___

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More written practice

1. ∫₀^21 (22x + 1) dx = ___ 2. Find critical points of f(x) = x² − 42x + 24 ___ 3. Related rates: radius grows 20 cm/s. Find dV/dt when r = 22. ___ 4. Find lim(x→24) (x² − 576)/(x − 24) = ___ 5. If f(x) = 24x³ − 25x, find f′(23) = ___ 6. ∫₀^24 (25x + 1) dx = ___

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Patterns and rules

1. Find lim(x→35) (x² − 1225)/(x − 35) = ___ 2. If f(x) = 35x³ − 36x, find f′(34) = ___ 3. ∫₀^35 (36x + 1) dx = ___

_See printable PDF for diagram._

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Stretch

1. Find lim(x→43) (x² − 1849)/(x − 43) = ___ 2. If f(x) = 43x³ − 44x, find f′(42) = ___

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Parent tip: Sketch graphs to check signs and behavior