The Final 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

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

 

Section

Objectives

Exercises

4.1

Understand antiderivative and its relation to derivative

3

 

Use indefinite integral notation for antiderivatives

11,17,21,29,35,39

 

Use basic integration rules to find antiderivatives

11,17,21,29,35,39

 

Write the general solution of a differential equation

5

 

Find a particular solution of a differential equation

55,59,71

4.3

Understand the concept of area of a plane region

17,19,27,31

 

Evaluate a definite integral using properties of the definite integral

33,41

4.4

Evaluate the definite integral using the Fundamental Theorem of Calculus

5,11,15,17,21,27,29,37,41,69

4.5

Use pattern recognition to evaluate an indefinite integral

3,5,7,11,17,23,25,35,43,45,47,49

 

Use a change of variables to evaluate an indefinite integral

63, 65

 

Use a change of variables to evaluate a definite integral

71, 73, 77

 

Evaluate a definite integral involving an odd or even function

101, 103

 

 

Part 2: with notebook

 

 

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

 

 

4.2

Use sigma notation to write and evaluate a sum

3,9,17

 

Understand the concept of area of a plane region

23,27

 

Approximate the area of a plane region

23,27

 

Understand and apply the concept of upper and lower sums

27, 45

 

Find the area of a plane region using limits

31,39,47,51

4.3

Understand the definition of the Riemann Sum

1,3,7,11

 

Evaluate a definite integral using limits

3,7,11

 

4.4

Understand the Mean Value Theorem for Integrals

43

 

Find the average value of a function over a closed interval

49

 

Understand and use the Second Fundamental Theorem of Calculus

75,81

 

           

Section

Objectives

Exercises

7.1

Set up and evaluate definite integral to find the area of a region in the plane

1, 3

 

Sketch the region bounded by the graphs of two functions and evaluate the definite integral to find the area of that region

7, 9, 17, 21, 25, 27, 35, 45

 

Find the area of a region by integrating (i) with respect to x and (ii) with respect to y

13

7.2

Set up and evaluate definite integral to find the volume of a solid formed by revolving a region about the x-axis

1, 5, 11a, 33

 

Set up and evaluate definite integral to find the volume of a solid formed by revolving a region about the y-axis

7, 9, 11b, 31