Limits

This is the most important topic in the module. Concept of limits is central to calculus. Emphasis is on conceptual understanding of limit, followed by a formal definition of limit. Pathological examples and further exploration of limits will be done during computer laboratory sessions to enhance further  conceptual understanding. Sufficient competency in the computating limits should be achieved. The definition of a limit will be served as an example of formulating mathematical ideas.

Syllabus

• Concept of limits.
• Formal definition of a limit. Illustration via examples to demonstrate the definition.
• Computation of limits via limit laws, factorization, rationalization.
• One-sided limits and piecewisely defined functions.
• Squeeze Theorem.
• lim(sin x/x) = 1 as x tends to 0.
• Limits at infinity and horizontal asymptotes. lim(1/x^n) = 0 as x tends to infinity.
• Infinite limits and vertical asymptotes.

Reference: NG TB, Calculus, Chapter 4.