Students learning calculus limit problems need to know what a limit of a function is before they can evaluate them. The concept of limits is finding the value of a function as x approaches a certain value, a. For example, in the linear function y = 3x-5, as x approaches 2, y takes on the value of 1. This is solved by substituting 2 into the function:
lim y = 3x – 5 = 3(2) - 5 = 6 - 5 = 1
Students should be shown graphs of the functions so they can understand the concept of limit. Limits may or may not be continuous at the value a in a graph. Textbooks are good sources of graphs showing continuous and discontinuous functions. If you have a smartboard you may want to try an online interactive gallery for graphing functions which can be found at: Maths Online from the University of Vienna, Austria. The limit theory should explain the limit of a function as x approaches from the left and right.
For example, in the function:
lim y = x2- 4, the function does not exist as the value x approaches 2, but the limit exists.
x→2 2 –x
The limit exists as the graph approaches from the left side and right side of the function. From the left and right side of the limiting x value 2, the y value is approaching -4.