Problem:
Compare the graphs of the functions

y = ex
and
y = (1 + x/n)n

for large values of the integer n.


Exploration:
Using the following LiveMath Notebook:

The red graph is the graph of the exponential function, y = ex, and the blue graph is the graph of the polynomial y = (1 + x/n)n.

Increase the values of the integer n in the Notebook above and see the effect on the blue graph.