Tutorial 2

Object: Learn how to determine whether a function is continuous or not.
 
(a) A function is left continuous at x=a if the left limit equals to f(a) or
                  
limx → a f(x) =  f(a)

(b) A function is right continuous at x=a if the right limit equals to f(a) or
                  
limx → a+ f(x) =  f(a)
(c) A function is  continuous at x=a if the  limit equals to f(a) or
                   
limx → a f(x) =f(a).
In particular,  the left limit and the right limit must exist and equals to each other, i.e
                     
limx → a+ f(x) =limx → a f(x) = limx → a f(x) =f(a)

               
     Open the following maplets.


  1. Left and Right Limits and Continuity, using a Graph 
    Learn to identify left and right limits, continuity from the left and right and their relation to 2-sided limits and continuity from the graph of the function.
  2. Left and Right Limits and Continuity, using a Formula
    Learn to identify left and right limits, continuity from the left and right and their relation to 2-sided limits and continuity from the formula for the function.