MATH 2250 (Chastkofsky) Spring 2008
Calculus I for Science and Engineering
Homework
Text: Hass, Weir, and Thomas, University Calculus
Chapter 2: Limits and Continuity
2.1 Rates of Change and Tangents to Curves
§2.1: #1, 11, 12, 15, 19
2.2 Limit of a Function and Limit Laws
§2.2: #1, 2, 3, 5, 9, 13, 19, 21, 22, 25, 27, 29, 34, 35, 36, 39, 42, 49, 57, 64, 65, 85
2.6 Continuity
§2.6: #1–4, 5–10, 13, 19, 25, 35, 36, 39
2.7 Tangents and Derivatives at a Point
§2.7: # 5, 7, 11, 13, 18, 23, 27, 28, 29, 30
Chapter 3: Differentiation
3.1 The Derivative as a Function
§3.1: #1, 3, 6, 9, 10, 13, 17, 31, 33, 43, 44
3.2 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients
§3.2: #1, 3, 5, 7, 11, 15, 17, 18, 21, 23, 24, 27, 28, 29, 33, 35, 39, 43, 47, 49,
50, 53, 58, 62, 63
3.3 The Derivative as a Rate of Change
§3.3: #1, 5, 7, 10, 11, 15, 17, 18, 21, 23, 26, 29
3.4 Derivatives of Trigonometric Functions
§3.4: #1, 5, 8, 9, 11, 13, 16, 20, 25, 27, 35, 37, 47
3.5 The Chain Rule and Parametric Equations [N.B. Skip parametric formula for
second derivatives]
§3.5: #1, 3, 5, 9, 11, 15, 17, 19, 24, 27, 31, 35, 41, 45, 47, 50, 51, 55, 57, 59,
61, 71, 73, 81, 83, 86, 95, 99, 112, 115
3.6 Implicit Differentiation
§3.6: #1, 5, 11, 17, 19, 25, 39, 44, 51
3.7 Derivatives of Inverse Functions and Logarithms
§3.7: #3, 11, 13, 21, 25, 27, 29, 32, 41, 51, 57, 61, 64, 65, 91, 93, 95, 98
3.8 Inverse Trigonometric Functions
§3.8: #1, 3, 7, 21, 23, 30, 33, 34, 42, 43, 48, 54
3.9 Related Rates
§3.9: #1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 22, 23, 25, 30, 31, 35
3.10 Linearization and Differentials
§3.10: #3, 8, 11, 15, 16, 39, 43, 45, 53, 54, 56, 61, 62
Additional Exercises: #6, 8, 19, 20
Chapter 4: Applications of Derivatives
4.1 Extreme Values of Functions
§4.1: #1–14, 15, 17, 19, 21, 25, 27, 29, 31, 33, 39, 41, 43, 49, 51, 55, 61, 72
4.2 The Mean Value Theorem
§4.2: #5, 6, 7, 9, 25, 27, 31, 35, 39, 41, 45
4.3 Monotonic Functions and the First Derivative Test
§4.3: #1, 3, 5, 7, 9, 13, 17, 21, 25, 31, 43
2.4 One-Sided Limits and Limits at Infinity
§2.4: #1, 2, 7, 10, 12, 17, 19, 20, 21, 23, 25, 27, 34, 35, 39, 43, 47, 49, 51, 55, 74
2.5 Infinite Limits and Vertical Asymptotes
§2.5: #1, 3, 9, 13, 14, 17, 18, 19, 23, 31, 35
4.4 Concavity and Curve Sketching
§4.4: #1, 3, 11, 15, 17, 21, 25, 30, 33, 37; p. 309: #55, 57, 59
4.5 Applied Optimization
§4.5: #1, 3, 4, 5, 7, 11, 12, 14, 20, 27, 32, 33, 41, 44
4.6 Indeterminate Forms and L’Hopital’s Rule
§4.6: #3, 5, 9, 15, 19, 21, 23, 25, 47, 51, 53, 61, 63
4.7 Newton’s Method
§4.7: #1, 3, 5, 13, 16
4.8 Antiderivatives
§4.8: #1, 5, 7, 13, 15, 19, 23, 31, 33, 39, 43, 45, 55, 59, 61, 65, 87, 89, 91, 95,
103, 117, 118, 119, 120
Chapter 5: Integration
5.1–5.2 Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums
§5.2: #1, 3, 7, 9, 13, 15, 19, 35,37,38, 39
5.3 The Definite Integral
§5.3: # 9, 11, 13, 17, 19, 27, 31, 35
5.4 The Fundamental Theorem of Calculus
§5.4: #1, 3, 5 11, 17, 23, 27, 29, 33, 35, 39, 41, 43, 45, 47, 49, 53, 55,
58, 61–64, 73, 75
5.5 Indefinite Integrals and the Substitution Rule
§5.5: #1, 3, 5, 7, 9, 13, 17, 19, 22, 23, 29, 39, 43, 49, 51, 61, 67
5.6 Substitution and Area Between Curves
§5.6: #1, 3, 7, 13, 25, 27, 31, 39, 47, 51, 53, 55, 57, 67, 77, 81, 85, 89, 99, 103