L’Hôpital’s Theorem

L’Hôpital’s Theorem can be used when evaluating limits that have a certain sort of “indeterminate form” (either $\frac{0}{0}$ or $\frac{\pm\infty}{\pm\infty}$). Subject to some other conditions (What are they? Make sure you check that they’re satisfied!), we can use L’Hôpital’s Theorem to calculate limits like

$$\lim_{x\to 0}\frac{\sin x}{x}$$

Use L’Hôpital’s Theorem to find the value of this limit for tomorrow’s lesson. Also, what do you think about the result shown below?

$$\lim_{x\to 0}\frac{\cos x}{x}=\lim_{x\to 0}\frac{-\sin x}{1}=0$$