LIMITS

Rate of change: 
Change in dependent variable with respect to change in independent variable.

In the function of y = f (x)

x is independent variable, y is the dependent variable.

Slope: 

Slope of secant: Average rate of change of y with respect to x over the interval from x = a to x = a + h
Slope of tangent: The slope of the tangent to the graph y = f (x) at point P (a, f(a))

If the slope of a line equal to m,
and then the slope of the line perpendicular to this line will be

Limits:

Left hand limit:
Right hand limit:
Limit:

If		then there is a limit.
If		then limit does not exist

Continuity

A function is continuous at a point when the graph passes through the point without a break.  If the graph has a break of some type at a point, then the graph is not continuous (discontinuous) at this point.

The function f (x) is continuous at x = a

If

= f (a)

Polynomial Functions:

P(x) = a_nxⁿ + a_n-1x^n-1 + ...a₁x + a₀

a₀, a₁, a₂...an are constant.

All the polynomial functions are have limits at all real values.

All the polynomial functions are continuous at all real values.

Rational Functions:

Every rational functions are continuous except at a value:  Q(a) = 0