Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.8 The Mean Value Theorem and l’Hôpital’s Rule, #35 · Calculus · Applications of derivatives

The figure for this exercise is in the book and isn't reproduced…

Stein's calculus book asks for the limiting ratio of $f (x) =$ triangular area $A B C$ to $g (x) =$ curved area $A B C$ .
(a) Guess the limit of $f / g$ as the angle $x$ goes to zero.
(b) Explain why $f (x)$ is $\frac{1}{2} (sin x - sin x cos x)$ and $g (x)$ is $\frac{1}{2} (x - sin x cos x)$ . (c) Compute the true limit of $f (x) / g (x)$ .

The figure for this exercise is in the book and isn't reproduced here.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.8 The Mean Value Theorem and l’Hôpital’s Rule, #35

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