Calculus lets you approximate complicated functions with power series. The Wolfram Language lets you generate and work with power series for a huge range of functions.

Use Series to make a power series out of a function. The first argument is the function. The second argument has the form {var,pt,order}, where var is the variable, pt is the point around which to expand, and order is the order:

The "big-O" notation O[x]⁶ indicates that terms beyond x⁵ are omitted:

Truncate the series to get a polynomial of degree 5 using Normal:

At , compare the polynomial and the original exponential function: