Study Suggestions and Suggested Exercises

Introductory Calculus, Fall 2006, Dr. LeMesurier

Chapter 4, Applications of Differentiation

Section 4.1 Maximum and Minimum Values, exercises 1, 2, 3, 5, 7, 11, 15, 21, 33, 49.

Section 4.2 The Mean Value Theorem, The main objective here is to understand the Mean Value Theorem, and its applications such as in Examples 4 and 5. Exercises 1, 17.

Section 4.3 How derivatives affect the shape of a graph, exercises 1, 3; 5; 11, 15; 23; 25; 29, 31, 43.

Section 4.4: l'Hospital's rule, is partly covered here; the part about indeterminate ratios like "0/0" and ∞/∞, which is up to Example 5. The rest, starting at "Indeterminate Products" is done in Calculus 2, Math 220. Try exercises 1, 3; 5; 11, 15; 23; 25; 29.

Section 4.5 Summary of Curve Sketching, exercises 1, 3, 13, and any others from 1-50.

Section 4.7 Optimization Problems, exercises 1, 5, 7, 9, 11, 15, 21.

Section 4.10 Anti-derivatives, exercises 1, 5, 9, 13; 17, 19, 23, 27.

Chapter 5, Integrals

Sections 5.1 Areas and Distances and the Definite Integral

These are introduced in a more concise form in my handout, which also includes exercises as a homework assignment. These notes emphasize the right end point approximation rule, and you need not study so much the case of arbitrary sample points. Some extra exercises from the text are
Section 5.1 Exercises 1, 3, 7, 11, 15, 19.
Section 5.2 Exercises 5, 7, 15.

Section 5.3 The Fundamental Theorem of Calculus, exercises 1, 3, 5, 9, 13.

Section 5.4 Indefinite Integrals and the Total Change Theorem, exercises 1, 5, 11, 19, 29, 47, 53.

Section 5.5 The Substitution Rule, exercises 1, 3, 5; 7, 13, 21, 49, 53, 63.


© 2006 Brenton leMesurier, College of Charleston, Department of Mathematics.
Revised October 31, 2006.