Extra lesson 1: L'Hopital's Rule

Before we start, lemme tell you about extra lessons, these are lessons which I won't be covering in much detail, and won't make a test on them. However, I will give you some resources from which you could study them.

L'Hopital's Rule is the most crucial rule in solving limits, as it is a workaround for indetermenint values like \(\frac{0}{0}\) or \(\frac{\infty}{\infty}\) but I didn't teach you this beforehand because it involves taking teh derivative of both sides of the fraction in the limit. For example: $$\lim_{x \to 0} \frac{x^2}{2x}$$ to evaluate this limit, you can take the derivative of both sides of the fraction as many times as you want: $$\lim_{x \to 0} \frac{\frac{d}{dx} x^2}{\frac{d}{dx} 2x}$$ $$\lim_{x \to 0} \frac{2x}{2}$$ $$\lim_{x \to 0} \frac{x}{1}$$ then plug in \(x = 0\) and you find that the limit as this function approches 0 is 0

Try It:

here are some resorces that you can us:

L'Hopital's Rule by Organic Chemistry Tutor
L'Hopital's Rule by Professor Leonard
L'Hopital's Rule by Three Blue One Brown (don't watch this unless u already understand l'hopital's rule and only need something to visulaize it)