Limit Exploration

The limit does not exist because as x approaches -4 from the left the limit is 0 but as x approaches -4 from the right the limit is 2. You cannot have two answers, therefore the limit does not exist.

Does the following function have a limit at a=0? If so, what is it?

The limit of f(x) as x approaches 0 is undefined but with estimations the limit is 1.

Does the following function have a limit at a=0? If so, what is it?

The limit of f(x) as x approaches 0 is undefined but with estimations the limit can be approximated to be 1.

The next function has a constant k in it that you can change with the slider. Find a value for k so that the limit of the function exists at every point. Answer: k=

k=2

Why does this value for k work? Explain what you see geometrically, and if possible explain algebraically. Answer:

The value of k=2 works because 2 is an intercept. When approaching from both the left ad the right the limit always goes to 0.

When you are done, save this graph and share it with me (dmarshall@nmhschool.org).