Find a d that satisfies the definition of the limit of

f(x) = 3x + 4

as x approaches a = 2 for various values of epsilon starting with e = 0.5.

In the following LiveMath Notebook, you can see the graph of y = f(x) in blue, the graphs of y = L + e and y = L - e in red and the graphs of x = a + d and x = a - d in green. Start with a = 2 and e = 0.5 and then find out which d would satisfy the definition of limit. Next, try different values for e and find the corresponding d's. Click here if you would like to see more information about using the following notebook.

Explore with changing a; consider a = 6, 8, 16 using the same epsilon's. Can you detect a pattern?

Change the slope and y-intercept and consider a = 6, 8, 16 using the same epsilon's again. Can you detect a pattern?.

Acknowledgment: This notebook is a modification of a similar notebook in the MathView User's Guide.