Intermediate Value Theorem

Suppose that f(x) is continuous on [a, b] and let M be any number between f(a) and f(b). Then there exists a number c such that,

1. 
2. 

Fact 2

If is continuous at and then

Fact 1

Because of the definition of continuity we can derive that:

If is continuous at then,

Types of Discontinuities.

Oscillating

Vertical Asymptotes

Removable

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Definition of Limit

A function is said to be continuous at if

A function is said to be continuous on the interval [a, b] if it is continuous at each point in the interval