Objectives and exercises

 

Textbook: Calculus, 8th edition, Larson/Hostetler/Edwards, Houghton Mifflin, 2006

 

Section

Objective

Exercises

P.3

Use f(x) notation to represent & evaluate functions

3, 7, 9

 

Find domain and range of f(x)

13, 15, 25, 27

 

Distinguish between relation & function

43

 

Identify and use transformations of functions

53, 55

 

Construct new functions using +, -, x, /, and composition & identify domain of new function

61, 63 a, c, e

 

Identify odd/even functions/ apply symmetry test

67, 69

 

Sketch the graph using information about domains, intercepts, symmetry, transformation of basic functions

31, 35

Section

Objectives

Exercises

1.1

understand tangent line problem

3

 

understand area problem

9, 11

1.2

estimate limit using numerical approach

1, 7

 

estimate limit using graphical approach

11, 13, 19

 

identify and explain when a limit fails to exist

21, 23

 

explain the formal definition of limit using linear functions

29, 33, 39

1.3

use properties of limits to evaluate limits

11, 17, 25, 29, 37

 

evaluate limits of rational functions by canceling common factors

43, 49

 

evaluate limits by rationalizing the numerator

53

 

use Theorem 1.9 to evaluate limits involving trig functions

67, 67

 

understand the Squeeze Theorem

87

 

applications of limits

101

1.4

understand, explain and use definition of continuity at a point

3, 5

 

continuity on an interval

29, 31

 

identify removable discontinuity points

37, 41

 

modify definition of function to be continuous at removable discontinuity

37, 41

 

understand concept of one-sided limits

7, 11,13

 

apply one-sided limit concept to determine existence of limit

5, 17

 

apply one-sided limit to continiuty on a closed interval

29, 31

 

understand and apply properties of continuous functions

59

 

understand and use concept of continuity of composite function

61

 

apply intermediate value theorem to determine existence of zeros of functions

83

1.5

determine infinite limits from the left and the right

33, 37 

 

identify vertical asymptotes using the limit of the function

11, 21

 

use the properties of limits to evaluate infinite limits

 59, 61

 

Section

Objectives

Exercises

 

2.1

find the slope of the tangent line to a curve

1, 7

 

 

use the limit definition to find the limit of a function

15, 17, 21

 

 

find the equation of the tangent line to the graph at a point

25, 33

 

 

understand the relationship between differentiability and continuity

71, 91

 

2.2

find derivative of a constant function

3

 

 

find derivative of function using the power rule

5, 7, 9

 

 

find derivative of function using the constant multiple rule

13, 15

 

 

find derivative of function using sum and difference rules

13, 15, 33, 43

 

 

find derivative of sine and cosine function

19, 21, 37, 51

 

 

use derivatives to find rates of change

89, 93

 

 

find equation of tangent line

53, 55

 

 

determine points at which graph has horizontal tangent line

59, 61

 

 

applications

93

 

2.3

find derivative of function using the product rule

3, 5, 35

 

 

find derivative of function using the quotient rule

9, 11, 25, 33

 

 

find derivative of a trigonometric function

5, 11, 43, 47

 

 

find higher-order derivatives

93, 97, 101

 

 

determine points at which graph has horizontal tangent line

73

 

 

find equation of tangent line

65, 67

 

 

use derivatives to find rates of change

83, 87

 

 

applications

87, 115125

 

2.4

find derivative of a composite function using the Chain rule

1, 5

 

 

find derivative of a function using the General Power rule

1, 7, 13, 27, 31

 

 

apply Chain rule to trigonometric functions

41, 47, 55

 

 

find equation of tangent line

67, 71, 73

 

 

find higher-order derivatives

83, 87

 

 

applications

101, 105

 

2.5

Distinguish between functions written in implicit form & explicit form

17

 

 

Use implicit differentiation to find the derivative of a function

1, 7, 11, 21, 25

 

 

find higher-order derivatives

45, 47

 

 

find equation of tangent line

33, 41

 

 

determine points at which graph has horizontal tangent line

57

 

2.6

find a related rate

1, 5, 15

 

 

use related rates to solve real-world problems

19, 25, 31, 39, 43

 

 

Section

Objectives

Exercises

3.1

Understand definition of extrema of a function on an interval

all assigned exercises

 

Understand definition of relative extrema of a function on open interval

1, 5, 7,11,15

 

Find relative extrema on an open interval

11, 13

 

Find absolute extrema on an closed interval

21,25,31,35,37, 59

3.2

Understand and use Rolle's Thm

5,9,15

 

Understand and use Mean Value Thm

31,43

3.3

Determine intervals on which a function is increasing or decreasing

3,13,21,27,29

 

Apply the First Derivative Test to find relative extrema of the function

13,21,27,29,33,41

3.4

Determine intervals on which a function is concave up or concave down

3,7

 

Find any points of inflection on the graph of a function

13,19,21,25

 

Apply the Second Derivative Test to find relative extrema of the function

27,37,39

3.5

Determine finite limits at infinity

1,3,5,13,15,19,25,29

 

Determine the horizontal asymptotes, if any, of a function's graph

35, 37, 57, 59

 

Determine infinite limits at infinity

1,3,5,13,15,19,25,29

 

Sketch the graph of an equation

57, 59

3.6

Analyze and graph the equation of a function

1-4,9,13, 21, 27, 31

 

 

 

3.7

Solve applied minimum and maximum problems

3,5,9,13,25,45

 

 

 

3.9

Understand the concept of a tangent line approximation

1,5

 

Compare the values of the differential dy with the actual change in y

7,9

 

Estimated a propagated error using a differential

29,35,41

 

Find the differential of a function using differential formulas

11,13,19