Guess the Limit Value...1

Calculus
Section 1.5





According to Wolfram, the limit is 0.
How can I guess the limit to be 0 from the table of values? I know there are techniques for finding the limit of functions but we are going chapter by chapter and section by section. Later on we will explore short cuts for finding the limit of functions. For Section 1.5, I will use a table of values for guessing the limit of functions.

 

according to Wolfram

here is how:

you are given: find lim((x^2-3x)/(x^2-9)), as x->3

first simplify (x^2-3x)/(x^2-9)

(x^2-3x)/(x^2-9)=x(x-3)/((x-3)(x+3)).......cancel (x-3) and you get x/(x+3)

 

Let's not use limit short cuts. I want to learn how to guess the limit using a table first. How is this done?