The Midterm Exam  is divided into two parts.  The following guidelines apply for the use of notebooks.

 

            Part 1: no notebook

            Part 2: with notebook

 

Part 1: no notebook

           

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

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

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

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

 

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

 

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

 

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

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

 

Part 2: with notebook

 

Section

Objectives

Exercises

1.2

explain the formal definition of limit using linear functions

29, 33, 39

1.3

use Theorem 1.9 to evaluate limits involving trig functions

67

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

 

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

determine points at which graph has horizontal tangent line

59, 61

 

 

applications

93

 

2.3

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, 115, 125

 

2.4

find higher-order derivatives

83, 87

 

 

applications

101, 105

 

2.5

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