Chapter 5.6, Problem 102E

Finding a Limit In Section 1.3, a geometric argument (see figure) was used to prove that $\underset{\theta \to 0}{\lim }\frac{\sin \theta }{\theta }=1$

(a) Write the area of $\Delta ABD$ in terms of $\theta$.

(b) Write the area of the shaded region in terms of $\theta$.

(c) Write the ratio R of the area of $\Delta ABD$ to that of the shaded region.

(d) Find $\underset{\theta \to 0}{\lim }R$.