Find Limit Graphically...4

[nycmathguy]

Find the limit using a graph.

Note: f(3) = 5 according to the graph. Yes?

Question: If there was a hole at f(3), then the limit DNE. Yes?

 

[MathLover1]

Notice again that the actual value of the function at 3 is not relevant to finding the limit

In this case, limx →3- f(x) = f(c), but lim x →3+ f(x) does not equal f(c). Also, because the limits are different from the left and from the right, the two-sided limit limx →3 f(x) does not exist. Specifically, we can write:

limx →3- f(x) =5

limx →3+ f(x) = 2

limx →3 f(x) does not exist

 

[nycmathguy]

Notice again that the actual value of the function at 3 is not relevant to finding the limit

In this case, limx →3- f(x) = f(c), but lim x →3+ f(x) does not equal f(c). Also, because the limits are different from the left and from the right, the two-sided limit limx →3 f(x) does not exist. Specifically, we can write:

limx →3- f(x) =5

limx →3+ f(x) = 2

limx →3 f(x) does not exist

It's ok to make mistakes when learning.