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?
\[\lim_{x\to 0}\frac{\cos x}{x}=\lim_{x\to 0}\frac{-\sin x}{1}=0\]