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Functions and Limits

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Calculus and Analytical Geometry
MTH101
LECTUER ­ 6
Functions and Limits
Although f is the symbol most common
In this lecture we shall discuss:
ly used to denote a function, any symbol can
be used. Thus
Example
y=4x+1 defines y as a function of x
because each value assigned to x determines
exactly one value of y.
Example
In the following example y is not a function
of x, as each value assigned to x determines
two values of y.
If we use the letter f to denote a function,
then the equation
Mth101
Page 17
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Calculus and Analytical Geometry
Functions and Limits
Example
x≥0
⎧x
Exampl
x =⎨
e
⎩- x
x<0
Natural Domain
If a function is defined by a formula and
there is no domain explicitly stated, then it is
understood that the domain consists of all real
numbers for which the formula makes sense,
and the function has a real value. This is called
the natural domain of the function.
Exampl
e
Mth101
Page 18
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