Unit 1: Limits and Continuity

Evaluate each limit or show it does not exist.

Let [math]

The function [math] satisfies [math] for all [math] near 0. Additionally, consider the piecewise function [math]

Consider the function [math] and the formal ([math]-[math]) definition of a limit.

Let [math] be a continuous function on [math] with values given in the table below.

Let [math].

Define [math] and [math] where [math] is the greatest integer function.

Evaluate each limit.

The position of a particle is given by [math] and [math] for [math], [math].

Let [math] and [math] be functions with the following properties: • [math] is continuous on [math] with [math] and [math] • [math] is continuous on [math] with [math] and [math] • [math] is invertible