Continuity

The main objective is to define continuity at a point, and understand the concept of continuity.  Two thereoms, namely the Internediate value Theorem and Extreme Theorem about functions defined and continuous on a closed and bounded interval [a,b] will be stated.

Syllabus

• Definition of continuity at a point.
• Properties of continuity. (for examples: Continuity is preserved under addition, product and composition of functions.)
• Continuity on interval.
• Intermediate Value Theorem.
• Extreme Value Theorem.
• Some consequences or applications of IVT and EVT.

Learning Objectives

• Students should be able to verify continuity at a point via definition.
• Students should know that x^n, trigonometric functions are continuous.
• Students should be able to verify continuity of some functions using properties of continuity.
• Students should understand the Intermediate Value Theorem. They should know how to read the statement, and apply the Intermediate Value theorem.

Reference: NG TB, Calculus, Chapter 4.