as it is only used immediately prior to a technique called improper integrals which we will cover in Math 101. However, the result is fundamentally one about making certain limits easier to compute, so we’ll cover it here in Math 100.
Module Learning Objectives.
Use L’Hospital’s Rule to compute the limit of functions in the indeterminate forms \(0/0\) and \(\infty/\infty\text{.}\)
Use L’Hospital’s Rule to compute the limit of functions in the indeterminate forms in exponential form like \(0^0\) and \(\infty^0\text{.}\)
Video4.5.1.L’Hospital’s Rule.
We’ve previously spent a lot of effort studying limits of the form 0/0 via algebraic tricks like factoring or common denominators. Now we learn how to leverage our knowledge of derivatives and the incredibly powerful L’Hôpital’s Rule.
Video4.5.2.L’Hospital’s Rule for other indeterminate forms.
We can’t directly apply L’Hôpital’s Rule to indeterminate forms like \(1^{\infty}\text{.}\) But that’s what logarithms are for!
