Midterm review, MATH 9B

The midterm is a closed book test. Calculators, cellular phones and helpful friends are NOT allowed.

For full credit you must justify your answers and show all steps.

You should be familiar with the material of Chapter 4, Section 4.3-4.6, Chapter 5 (without Section 5.10) and the first Section in Chapter 6.

Example questions:

1. (Integration) (Fundamental Theorem of Calculus, Second Fundamental Theorem of Calculus, Mean Value Theorem for Integration)
   1. (Section 4.4) Theorems 4.9-4.11
   2. (Exercises to Section 4.4) Problems 69, 73, 75
2. (Definite Integral, Definite Integrals determine the area, Integration of even and odd functions)

   (Exercises to Section 4.4) Problems 15, 21, 24, 25, 29, 39, 41

   (Section 4.5) Theorem 4.15, Example 10

3. (Natural logarithm, logarithmic differentiation)

   (Section 5.1) Example 6

   (Exercises to Section 5.1) Problems 51, 53,66, 85, 87

   (Exercises to Section 5.2) 5, 7, 11, 23, 29

4. (Inverse functions)

   (Section 5.3) Theorem 5.9, Example 5

   (Exercises to Section 5.3) 19, 25, 49

5. (Exponential function, Bases other than $e$)

   (Exercises to Section 5.4) 6, 39, 41, 83, 89

   (Exercises to Section 5.5) 9, 33, 47

6. (Differential equations)

   (Exercises to Section 5.6) 3, 5

   (Exercises to Section 5.7) 47, 51, 73

7. (Inverse Trigonometric functions)

   (Exercises to Section 5.8) Problems 33, 47, 49

   (Exercises to Section 5.9) Problems 3, 7, 23, 33, 35

8. (Area of a region between two curves)

   (Exercises to Section 6.1) Problems 15, 17, 20