AP Calculus BC : Continuity in Terms of Limits
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Example Questions
Example Question #1 : Limits And Continuity
The graph above is a sketch of the function 
For a function to be continuous at a point 
This is true for all values of 
Therefore, the interval of continuity is 
Example Question #3 : Limits And Continuity
Consider the piecewise function:
What is 
Limit does not exist.
Limit does not exist.
The piecewise function
indicates that 
The limit does not indicate whether we want to find the limit from the left or right, which means that it is necessary to check the limit from the left and right. From the left to right, the limit approaches 1 as 
Since the limits do not coincide, the limit does not exist for 
Example Question #4 : Limits And Continuity
Consider the function 
Which of the following statements are true about this function?
I.
II.
III.
III only
II only
I and III
I and II
I and II
For a function to be continuous at a particular point, the limit of the function at that point must be equal to the value of the function at that point.
First, notice that
This means that the function is continuous everywhere.
Next, we must compute the limit. Factor and simplify f(x) to help with the calculation of the limit.
Thus, the limit as x approaches three exists and is equal to 
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