# Module 3: Additional Integration Techniques and Limits

In this module, you will learn additional integration techniques and limits. The module content is split into four lessons.

### Show Your Work Problems

Module 3 assignment

### Other Information

Project 3:
Trying to evaluate $\inline \lim _{k\rightarrow \infty }\frac{e^{k}}{k^{!}}$ raises a problem: we definitely have the indeterminate form $\inline \frac{\infty }{\infty }$ but we can’t use L’Hospital’s Rule since the denominator’s factorial is not a differentiable function.

1. Search the internet to find a reasonably reliable web site or page that gives a definition of two functions having asymptotic equivalence (aka being asymptotically equivalent). Submit the definition and the web site/page you used as a reference.
2. Search the internet to find some version of Stirling’s Formula (aka Stirling’s Approximation). Submit the formula and the web site/page you used as a reference.
3. Use Stirling’s Formula to evaluate $\inline \lim _{k\rightarrow \infty }\frac{e^{k}}{k^{!}}$.