QuestionCalculate the average rate of change of $h(t)=\cot t$ over the intervals: a. $\left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right]$, b. $\left[\frac{5 \pi}{6}, \frac{3 \pi}{2}\right]$.

Studdy Solution
Calculate the average rate of change over the interval $\left[\frac{5 \pi}{6}, \frac{3 \pi}{}\right]$.
$$\frac{0 - (-\sqrt{3})}{\frac{3 \pi}{} - \frac{5 \pi}{6}} = \frac{\sqrt{3}}{\frac{3 \pi}{} - \frac{5 \pi}{6}} = \frac{\sqrt{3}}{\pi}$$So, the average rate of change over the interval $\left[\frac{5 \pi}{6}, \frac{3 \pi}{}\right]$ is $\frac{\sqrt{3}}{\pi}$.