NEKG33 Mathematical methods for economists

Chapter 16 : Day 16

By Lund University

Today we will learn about limits. Do you remember how the "lim" appeared in the definition of the derivative? Well, it's time to take it on. Oh yeah, a bit on continuity as well.

Limits and continuity

The main objective of this chapter is to study the derivative of a function. However, in order to understand the definition of a derivative we must look at limits. The limit of a function is the value that a function takes when x gets close to, but is not exactly equal to, a given value. Limits are closely related to another concept called continuity. Informally, a function is continuous if its graph is “connected”.

Rough introduction to limits

Rough introduction to limits at infinity

Rough introduction to infinite limits

Rough introduction to continuity

Limit laws

Continuity laws

Limits and continuity: Problems

Exercises on limits and continuity

Problem: Calculate limits

Problem: Calculate limits

Problem: Calculate limit

Problem: Calculate limit by trying a small value

Problem: Calculate limit by trying a small value

Problem: Calculate limit

Problem: Determine if a function is continuous

Problem: Determine if a function is continuous

Problem: Determine if a function is continuous

Problem: Make a function continuous