Section |
Topics |
Suggested Problems |
2.5 |
- Definition of continuity at a point
- How continuity can fail
- Examples of continuous functions
- Intermediate Value Theorem
|
- 10, 11, 13, 37
- 5, 6, 15, 18
- 21, 23, 24
- 47, 49, 50
|
2.6 |
- Calculating limits as x → ± ∞
- Horizontal and vertical asymptotes
|
- 15, 16, 17, 18, 20, 21, 30, 31, 33
- 5, 6, 39, 40
|
2.7 |
- Definition of derivative as limit of a difference quotient
- Derivative equals rate of change
- Slope of a curve; tangent lines
- Velocity = derivative of position
|
- 1
- 40, 46
- 5, 7, 9, 17
- 11, 13, 14, 37
|
2.8 |
- The derivative is a new function
- Various notations for derivative
- Differentiability implies continuity
- How a function can fail to be differentiable
|
- 3, 5, 6, 7, 14, 19, 20, 21, 41, 42
- 35, 36
|
3.1 |
|
- 3 – 22, 33, 34, 37, 39, 42, 45
|
3.2 |
- Calculating with the Product Rule
- Calculating with the Quotient Rule
|
- 3, 4, 9, 17, 27
- 5, 6, 7, 8, 13, 16, 32
|
3.3 |
- Derivatives of the six trig functions
- Calculating derivatives that involve trig functions
|
- 1, 17, 18, 19
- 1 – 10, 13, 16, 25, 28
|
3.4 |
- Recognizing compositions in a function
- Calculating with the Chain Rule
|
- 1 – 6
- 7 – 18, 23, 25, 29, 32, 34, 47, 49, 51
|
3.5 |
- Calculating derivatives of implicit functions
- Finding derivatives involving inverse tangent
|
- 1, 2, 3, 7, 11, 12, 17, 20, 25, 29
- 45, 46, 56
|