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Calculus
and Analytical
Geometry
MTH101
LECTUER
12
Continuity
Function
has different functional and
limiting
values
at x =c
Discontinuous:
as f(x) is not
defined
at x = c
Discontinuous:
as f(x) has a gap
at
x = c.
Discontinuous:
not defined at x = c.
Mth101
Page
34
Calculus
and Analytical
Geometry
Continuity
Example
Example
By
definition of g
Example
So,
f is continuous at x = c
Mth101
Page
35
Calculus
and Analytical
Geometry
Continuity
Proof
(c)
F is continuous at x = a,b
Example
(a)
F is discontinuous at x = a
(b)
F is discontinuous at x = b
Mth101
Page
36
Calculus
and Analytical
Geometry
Continuity
Example
Also
Example
This
equation cannot be solved
readily
by
factoring because the left
side has
no
simple factors.
Mth101
Page
37
Table of Contents:
- Coordinates, Graphs and Lines
- Absolute Values
- Coordinate Planes and Graphs
- Line and Definition of Slope
- Distance, Circles, Quadratic Equations
- Functions and Limits
- Operations on Functions
- Graphs of Functions
- Limits (Intuitive Introduction)
- Limits and Computational Approach
- Limits: A Rigorous Approach
- Continuity
- Limit and Continuity of Trigonometric Functions
- Tangent Lines and Rates of Change
- The Derivative