Introduction to the Limit of a Function: Apply It

  • Understand how to write the limit of a function using the correct symbols and estimate limits by examining tables and graphs
  • Understand one-sided limits (approaching a point from only one direction) and how they relate to two-sided limits
  • Understand and use the proper notation for infinite limits and define vertical asymptotes

The number e is a constant that, like π, is irrational (it cannot be represented as a ratio of integers) and transcendental (it is not the root of a non-zero polynomial of finite degree with rational coefficients). It was first discovered by the Swiss mathematician Jacob Bernoulli in 1683 while studying compound interest. It has many real-world applications including probability theory and exponential growth and decay. Below is an approximation of e to 20 decimal places.

e2.71828182845904523536

This number is perhaps best defined by a limit. Consider the function f(x)=(1+x)1x. We cannot compute f(0), but we can see what happens with values of x close to zero.