L'Hôpital's Rule
L'Hopital's Rule is a theorem dealing with limits that is very important to calculus.
Theorem
The theorem states that for real functions , if Note that this implies that
Proof
- No proof of this theorem is available at this time. You can help AoPSWiki by adding it.
Video by 3Blue1Brown: https://www.youtube.com/watch?v=kfF40MiS7zA
Text explanation:
let where and are both nonzero function with value at
(for example, , , and .)
Note that the points surrounding z(a) aren't approaching infinity, as a function like might at
The points infinitely close to z(a) will be equal to
Noting that and are equal to and respectively. This means that the points approaching at point a where and are equal to 0 are equal to $\frac{f'(x)}{g'(x)}
Problems
Introductory
- Evaluate the limit (weblog_entry.php?t=168186 Source)