Limits Overview
The first concept that calculus introduces to you is the idea of a limit. A limit is really just the extension of the algebraic concept of a function value or what I call the dot on the graph. When you were in algebra to graph an equation, someone gave you an equation, some y = _____ or f(x) = _____ , and then, using that equation, you would plug in x-values to find the y-values (function value). You would then graph those points, ( x , y ) , to find out what the graph looked like.
Meaning: Limit
A limit is asking you to determine, as you head towards a specific x-value , what y-value does it look like you are heading towards?
– A limit does not care if there is an actual function value (dot on the graph) at that x-value , it only cares about what y-value does it look like you are heading towards.
Remember that the answer to a limit question is always the y-value that it looks like you are heading towards.
You will be asked to find limits either given a graph , f(x) , to work from, or given an equation , f(x) , to work from.