This activity leads students through the process of discovering various definitions for Euler's constant 'e'. The first of these is related to differentiation, the second is related to integration. Then at the end are two extension tasks which give definitions based upon infinite sequences and series.
As a whole this task should give your students insights into the mathematical origins of this interesting and pervasive number.
The TI-Nspire document has 37 pages and includes full instructions for students There is also a single-page worksheet giving an introduction and overview of the activity.