Math1014 Practice Problems
Answers of odd problems are available in the textbook.
- Week One
- 6.1. Areas between curves.
- odd problems: 3, 9, 23, 31, 45.
- even problems: 10, 26, 28, 36, 46.
- 6.2. Volumes.
- odd problems: 3, 5, 9, 15, 23, 25, 41, 49, 51, 57,69.
- even problems: 6, 8, 12, 30, 44,56, 64, 66.
- Week Two
- 6.3. Volumes by cylindrical shells.
- odd problems: 1, 5, 9, 15, 29, 43.
- even problems: 2, 4, 14, 28, 32, 46.
- 6.4. Work.
- odd problems: 3, 5, 7, 13, 15, 23, 27, 29.
- even problems: 10, 16, 20.
- 6.5. Average value of a function.
- odd problems: 5, 7, 9, 13, 15, 17, 19.
- even problems: 16, 20, 24.
- Week Three
- 8.1. Arc length
- odd problems: 7, 13, 15, 21, 25, 35.
- even problems: 4, 20, 40.
- 8.2. Area of a surface of revolution
- odd problems: 3, 5, 15, 25, 29.
- even problems: 2, 26, 34.
- Week Four
- 7.1. Integration by parts.
- odd problems: 1, 3, 5, 7, 11, 15, 17, 29, 33, 49,61, 65, 67.
- even problems: 20, 26, 30, 34, 48,50, 54, 58,70.
- 7.2. Trigonometric integrals.
- odd problems: 5, 9, 13, 15, 17, 19, 25, 29, 31, 41, 43.
- even problems: 4, 6, 10, 16, 44, 48,66, 68, 70.
- Week Five
- 7.3. Trigonometric substitution
- odd problems: 3, 5, 7, 9, 13, 19, 21, 23, 25, 41.
- even problems: 12, 18, 24, 30, 38, 40, 42, 44.
- 10.3. Polar Coordinates
- odd problems: 1, 3, 5, 11, 17, 23, 39, 43, 45, 59, 77.
- even problems: 16,54,62, 66.
- 10.4. Areas and lengths in polar coordinates
- odd problems: 5, 13, 27, 31, 37.
- even problems: 6, 12, 32, 44, 56.
- Week Six
- 7.4. Partial fractions
- odd problems: 9, 17, 25, 37, 39, 47, 59, 61.
- even problems: 20, 22, 42, 62.
- 7.5. Strategy for integration
- odd problems: 5, 7, 19, 31, 43, 65, 77, 81.
- even problems: 22, 36, 48, 70.
- Week Seven
- 7.7. Approximation Integration
- odd problems: 1, 3, 17, 29, 35, 37, 47.
- even problems: 2, 6, 22, 30, 40, 48.
- 7.8. Improper integrals
- odd problems: 1, 5, 7, 9, 11, 13, 15, 19, 21, 25, 29, 39, 51, 71.
- even problems: 2, 8, 14, 26, 28, 36, 40, 50, 52, 62, 78.
- Week Eight
- 11.1. Sequences
- odd problems: 5, 7, 13, 15, 23, 25, 33, 35, 37, 49, 65, 69, 73, 81, 91.
- even problems: 24, 28, 38, 68, 78.
- 11.2. Infinite Series
- odd problems: 7, 11, 13, 19, 25, 27, 29, 37, 39, 49, 73.
- even problems: 18, 32, 34, 40, 50, 72, 90.
- Week Nine
- 11.3. Integral tests
- odd problems: 1, 5, 13, 21, 27, 29, 33, 37, 39.
- even problems: 6, 20, 22, 28, 44.
- 11.4. Comparison tests
- odd problems: 3, 5, 9, 15, 25, 31,37, 39.
- even problems: 12, 20, 30, 32,40, 46.
- 11.5. Alternting series
- odd problems: 3, 7, 13, 17, 23, 31.
- even problems: 8, 14, 26, 32, 36.
- Week Ten
- 11.6. Absolute convergence, ratio and root tests
- odd problems: 1, 3, 5, 13, 15, 23, 25, 35.
- even
problems: 8, 22, 28, 30, 32, 42.
- 11.7. Testing series
- odd problems: 3, 7, 9, 15, 23, 27, 33, 37.
- even problems: 8, 22, 28, 30, 36.
- 11.8. Power series
- odd problems: 5, 7, 13, 15, 17, 21, 23.
- even problems: 8, 12, 18, 22, 24, 42.
- Week Eleven
- 11.9. Representing of functions as power series
- odd problems: 5, 7,11, 23, 25, 29, 37, 41.
- even problems: 16, 30, 34, 40, 42.
- 11.10. Taylor and Maclaurin series
- odd problems: 5, 13, 25, 35, 43, 47, 53, 55, 69.
- even problems: 6, 10, 28, 48, 68, 70.
- 11.11. Applications of Taylor polynomials
- odd problems: 19, 25,29, 37.
- even problems: 36, 38.
- Week Twelve
- 12.1. Three-dimensional coordinate systems
- odd problems: 3, 5, 7, 9, 13, 17, 21, 41.
- even problems: 8, 14, 30, 42.
- 12.2. Vectors
- odd problems: 1, 3, 7,11, 17, 21, 23, 25, 27, 31, 45, 47
- even problems: 32., 38, 48.
- Week Thirteen
- 12.3. Dot product
- odd problems: 3, 7, 9, 21, 23, 25, 31,35,41, 45, 49,53.
- even problems: 10, 26, 28, 50, 52, 64.
- 12.4. Cross product
- odd problems: 3, 11, 13, 15, 19, 29, 33, 35, 37, 39, 45.
- even problems: 16,18, 38, 44, 46, 50, 52.