Explore graphically the limit

for various values of **a** and **b**.

In the following LiveMath Notebook, you can see the graph of

for **a = 2** and **b = 4** in blue. If **L** is the limit above,
the red line is the graph of **y = L + e** and
the green line is the graph of **y = L - e**.

By making the values of **e** smaller positive numbers, see if you can determine graphically what is the value of **L**.

Explore with changing **a** and **b**; consider **(a, b) = (1, 1), (1, 2),
(-2, 1), and (6, 2)** and calculating the corresponding limits **L**. Can you detect a pattern so that you can evaluate **L** without knowing the particular values of **a** and **b**?