ZeePedia

Absolute Values

<< Coordinates, Graphs and Lines
Coordinate Planes and Graphs >>
img
Calculus and Analytical Geometry
MTH101
LECTUER ­2
Absolute Values
Example
In this lecture we shall discuss:
Solve
SQUARE ROOTS AND ABSOLUTE VALUES
Example
Since 5>0
Since ­4/7 0
Since 0>0
Remark
1a1 is a nonnegative number for
all
values of a and
Exampl
e
Solve
Solution
Mth101
Page 4
img
Calculus and Analytical Geometry
Absolute Values
From theorem
1.2.2
Examples
Exampl
e
The inequality
The result (b) of above theorem can
be extended to three or more factors.
On real line
Geometric interpretation
of
Absolute Value
Example
Solve
Where A and B are points with coordinate
a and b. The distance between A and B
is
On combining these two sets
On real line
Mth101
Page 5
img
Calculus and Analytical Geometry
Absolute Values
Since for any real number a and b,
we know that
Now we have two
cases:
And
Mth101
Page 6
Table of Contents:
  1. Coordinates, Graphs and Lines
  2. Absolute Values
  3. Coordinate Planes and Graphs
  4. Line and Definition of Slope
  5. Distance, Circles, Quadratic Equations
  6. Functions and Limits
  7. Operations on Functions
  8. Graphs of Functions
  9. Limits (Intuitive Introduction)
  10. Limits and Computational Approach
  11. Limits: A Rigorous Approach
  12. Continuity
  13. Limit and Continuity of Trigonometric Functions
  14. Tangent Lines and Rates of Change
  15. The Derivative