Concept of limit - Definition

Author:YK Lau

Part I

Recall:

if for every number

, there exists a corresponding number

such that for all

. Illustration: 1. Check the box for

- challenge for

2. Move

on the

-axis 3. Use the vertical slider to give different

- challenge 4. Use the horizontal slider to adjust

so that the

- challenge is passed. Observation: For choices

, they fail the

- challenge.

Aim: To check that

is the limit of

. (i) Uncheck the box for

- challenge for

(ii) Check the box for

- challenge for

(iii) Repeat Steps 3 & 4 Observation: For the choice of

, the

- challenge is passed! So