Calculus, 9th edition

1
Calculus, 9th edition

• Varberg, Purcell Rigdon

2
Chapter 0

• Preliminaries

3
.1

• Real Numbers, Estimation, Logic

4
In calculus, the principle numbers are real
numbers.

• Be able to calculate with rational numbers
  (expressed as either repeating or terminating
  decimals) or irrational numbers (decimals that do
  NOT terminate or repeat)
• Be able to ESTIMATE answers before pushing a
  button on a calculator! Use good mental
  mathematics.
• Much done in math must be proven, and different
  methods of proof can be employed.

5
0.2

• Inequalities and Absolute Value

6
Solving inequalities

• Solve by comparing the inequality to zero, factor
  if possible, and solve.

7
Solving Absolute Value

• Consider absolute value as distance, if the
  distance is greater than a constant, you must get
  further away in both directions. If the distance
  is less than a constant, the solution values must
  be within a certain range of values.

8
0.3

• The Rectangular Coordinate System

9
Cartesian Coordinate System

• Graphs are done in the x-y system. You can find
  distance between any 2 points using Pythagorean
  theorem and midpoint of 2 any 2 points simply as
  the average.
• In both instances, a graph is often helpful in
  understanding the situation, prior to calculating.

10
Linear Equations

• General form Ax By C 0
• Slope-intercept form y mx b
• Point-slope form y y1 m(x x1)

11
0.4

• Graphs of Equations

12
Quadratic functions

• Graphs to a parabola
• Vertex at (h,k)
• Graph has reflection symmetry

13
Cubic Functions

• Reflects through the origin

14
0.5

• Functions Their Graphs

15
Functions

• Domain (x-values) real numbers which can be
  placed for x
• Range (y-values) real numbers which are created
  from the values for x
• Even functions Reflect through the y-axis, f(x)
  f(-x)
• Odd functions Reflect through the origin, f(x)
  -f(-x)

16
0.6

• Operations on Functions

17
Functions can be added, subtracted, multiplied or
divided

• Only consideration? Operations cannot result in a
  zero denominator
• Composition of functions When g is composed on
  f, the range of f becomes the domain for g.

18
0.7

• Trigonometric Functions

19
For all pts, (x,y) on the unit circlesin t y,
cos t x, tan t y/x

• t real number (length of arc on unit circle)
  that corresponds to pt (x,y)
• y sin x y cos
  x

20
Other trig functions

• sec x 1/cos x csc x 1/sin x
• cot x 1/tan x
• Pythagorean identity (main one, others may be
  developed from this one)