Q. 13 - Calculus

Question

Sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.8 in the reading. Your graph should include two different δ-bars and a graphical reason why they combine to make a punctured delta interval 

Step-by-Step Solution

Answer

Step 1. Given information.

We have to sketch a labeled graph that illustrates what is going on in the proof of Theorem 1.8 in the reading. 

Step 2. Sketch the graph

Theorem 1.6 says that for a limit to exist, the left and right limit must be exist and equal.

For the L.H.S. limit the graph is:

 

For the R.H.S. limit the graph is :

Now combining both the figures we have :