HINTS FOR TEACHING CALCULUS WITH APPLICATIONS
Algebra Reference Some instructors obtain best results by going through this chapter carefully at the beginning of the semester. Others nd it better to refer to it as needed throughout the course. Use whicheve
Chapter 13
THE TRIGONOMETRIC FUNCTIONS
13.1 Denitions of the Trigonometric Functions
17. Let = the angle with terminal side through (3; 4): Then x = 3; y = 4; and p p r = p x2 + y 2 = (3)2 + (4)2 = 25 = 5: 4 y = r 5 x 3 cos = = r 5 4 y tan = = x 3 sin = c
PRETESTS AND ANSWERS
CALCULUS WITH APPLICATIONS
Name:
Pretest, Form A
1. Evaluate the expression x2 + 3y z 3 when x = 2, y = 3, and z = 1. Perform the indicated operations. 2. 2x2 3x + 7 5x2 8x 9 3. (y 4)2 4. (2x 1) x2 + 3x 4 5. (5a + 2b) (5a 2b) Factor e
CALCULUS WITH APPLICATIONS
Name:
Pretest, Form B
Choose the best answer. 1. Evaluate the expression (a)
12 5 y2 z x2 +6
when x = 2, y = 4, and z = 8. (c) 12 (d)
4 5
1.
(b) 4
Perform the indicated operations. 2. x2 3x + 7 + 4x3 6x2 5x + 4 (a) 4x3 6x4 8x2 +
FINAL EXAMINATIONS AND ANSWERS
CALCULUS WITH APPLICATIONS
Name:
Final Examination, Form A
1. Find the coordinates of the vertex of the graph of f (x) = 2x2 + 30x + 45. 2. Write the equation 2a = d using logarithms. 3. Graph the function y = log2 (x 3) + 4
ANSWERS TO FINAL EXAMINATIONS
25
ANSWERS TO FINAL EXAMINATIONS
FINAL EXAMINATION, FORM A 1. (7.5, 157.5) 2. log2 d = a 3. 15. (x + 4) ex 16. Absolute maximum of 0 at 0; absolute minimum of 16 at 2 17. 20,000 18.
dy dx
=
314x1/2 y 14x3/2 +30x1/2 y2
19. 12
CALCULUS WITH APPLICATIONS
Name:
Final Examination, Form B
Choose the best answer. 1. Find the coordinates of the vertex of the graph of f (x) = 2x2 + 10x 17. (a) 5 59 , 2 2 (b) 5 59 , 2 2 (c) (5, 42) (d) (5, 42) 1.
2. Write the equation mp = q using loga
Introductory Organic Chemistry
2323.003
Rearrangments, E1 Reactions and
Reaction Comparisons
Prof. Christina Thompson
October 11th, 2016
Lecture 15
Rearrangements
Carbocations can rearrange to form a more stable
carbocation.
Move the smallest group on t
Introductory Organic Chemistry
2323.003
Review for Exam 1
Prof. Christina Thompson
September 20th 2016
Lecture 9
EXAM 1
Will Cover Chapters 1, 2, 3 and 5
(NOT CHAPTER 4)
EXAM WILL OCCUR IN ROOM:
HH 2.402
(the big auditorium)
Quiz 2 Results
Average ~39
G
Chapter 11
PROBABILITY AND CALCULUS
11.1 Continuous Probability Models
3. f (x) = 12 x ; [1; 4] 21 Since x2 0; f (x) 0 on [1; 4]: 1 21 Z
1 4
1 1 1. f (x) = x ; [2; 5] 9 18 Show that condition 1 holds. Since 2 x 5; 2 1 5 x 9 9 9 1 1 1 1 x : 6 9 18 2 Hence,
Chapter 10
DIFFERENTIAL EQUATIONS
10.1 Solutions of Elementary and Separable Dierential Equations
5. y dy = x2 dx Separate the variables and take antiderivatives. Z Z y dy = x2 dx x3 y2 = +K 2 3 2 y 2 = x3 + 2K 3 2 y 2 = x3 + C 3 6. dy = x2 x dx y dy = (x
Chapter 1
LINEAR FUNCTIONS
8. 4x + 7y = 1
1.1
Slopes and Equations of Lines
Rewrite the equation in slope-intercept form. 7y = 1 4x 1 1 1 (7y) = (1) (4x) 7 7 7 14 y= x 77 4 1 y = x+ 7 7 The slope is 4 : 7 9. x = 5 This is a vertical line. The slope is und
Chapter 2
NONLINEAR FUNCTIONS
9. y = 2x + 3
2.1
Properties of Functions
x y
2 1
1 1
0 3
1 5
2 7
3 9
1. The x-value of 82 corresponds to two y-values, 93 and 14. In a function, each value of x must correspond to exactly one value of y: The rule is not a fu
Chapter 3
THE DERIVATIVE
3.1 Limits
f (x) does not exist. The answer is c. 2. Since lim f (x) = lim f (x) = 1; +
x!2 x!2 x!2 x!2 x!2+ x!2
8. (a) By reading the graph, as x gets closer to 3 from the left or right, g(x) gets closer to 2. lim g (x) = 2
1. Si
Chapter 5
GRAPHS AND THE DERIVATIVE
5.1 Increasing and Decreasing Functions
(a) increasing on (1; 1) and (b) decreasing on (1; 1): 2. By reading the graph, f is (a) increasing on (1; 4) and (b) decreasing on (4; 1): 3. By reading the graph, g is (a) incre
Chapter 7
INTEGRATION
Z
7.1
Antiderivatives
10.
(5x2 6x + 3) dx Z =5 = = x2 dx 6 Z x dx + 3 Z x0 dx
1. If F (x) and G(x) are both antiderivatives of f (x), then there is a constant C such that F (x) G(x) = C: The two functions can dier only by a constant.
Chapter 8
FURTHER TECHNIQUES AND APPLICATIONS OF INTEGRATION
Z
8.1
Z 1.
Integration by Parts
xex dx and u = x: dv = ex dx Z Then v = ex dx and du = dx: Let v = ex Use the formula Z u dv = uv Z xex dx = xex Z ex dx = xex ex + C Z Z (x + 6)ex dx Let dv = ex
Chapter 9
MULTIVARIABLE CALCULUS
9.1 Functions of Several Variables
p 9(1000) + 5(0) (c) f (1000; 0) = log 1000 p 9000 = 3 p = 10 10 q 1 9 10 + 5(5) 1 ;5 = (d) f 1 10 log 10 p 25:9 = 1 p = 25:9 5. x + y + z = 9 If x = 0 and y = 0; z = 9: If x = 0 and z =
Introductory Organic Chemistry
2323.003
Intermediate Stability,
The Hammond Postulate and Carbon Ions
Prof. Christina Thompson
September 27th, 2016
Lecture 11
Exam 1
Average Score = 179
(72%)
5 points better than
last years class
If youre keeping
score
Pr