Chapter 1.6, Problem 40ES

In the circle in the accompanying figure, a central angle of measure $\theta$ radians subtends a chord of length $c\left(\theta \right)$ and a circular arc of length $s\left(\theta \right)$ . Based on your intuition, what would you conjecture is the value of ${\lim }_{x\to 0^{+}}c\left(\theta \right)/s\left(\theta \right)$ ? Verify your conjecture by computing the limit.