Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.8 The Mean Value Theorem and l’Hôpital’s Rule, #24 · Calculus · Applications of derivatives

l'Hôpital's Rule still holds for …: … is …\lim \frac{f(x)}{g(x)}=\lim \frac{1/g(x)}{1/f(x)}=\lim \frac{g'(x)/g^2(x)}{f'(x)/f^2(x)}=L^2\lim…

l'Hôpital's Rule still holds for $f (x) / g (x) \to \infty/\infty$ : $L$ is
$lim \frac{f ( x )}{g ( x )} = lim \frac{1/ g ( x )}{1/ f ( x )} = lim \frac{g ^{'} ( x ) / g ^{2} ( x )}{f ^{'} ( x ) / f ^{2} ( x )} = L^{2} lim \frac{g ^{'} ( x )}{f ^{'} ( x )} .$
Then $L$ equals $lim [f^{'} (x) / g^{'} (x)]$ if this limit exists. Where did we use the rule for $0/0$ ? What other limit rule was used?

~8 minWritten answer · check your work with Lemma

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.8 The Mean Value Theorem and l’Hôpital’s Rule, #24

Stuck? A gentle nudge

No hints for this one.

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.