Find the average rate of change of the function over the given interval.
-$$h ( t ) = \sin ( 5 t ) , \left[ 0 , \frac { \pi } { 10 } \right]$$
A) $- \frac { 10 } { \pi }$
B) $\frac { \pi } { 10 }$
C) $\frac { 5 } { \pi }$
D) $\frac { 10 } { \pi }$

Question

Quizplus · Accepted Answer

The average rate of change of a function $h(t)$ over an interval $[a, b]$ is given by $\frac{h(b) - h(a)}{b - a}$. For $h(t) = \sin(5t)$ over the interval $[0, \frac{\pi}{10}]$, we calculate $\frac{\sin(5(\frac{\pi}{10})) - \sin(5(0))}{\frac{\pi}{10} - 0} = \frac{\sin(\frac{\pi}{2}) - \sin(0)}{\frac{\pi}{10}} = \frac{1 - 0}{\frac{\pi}{10}} = \frac{10}{\pi}$.

Find the Average Rate of Change of the Function Over h(t)=sin⁡(5t),[0,π10]h ( t ) = \sin ( 5 t ) , \left[ 0 , \frac { \pi } { 10 } \right]h(t)=sin(5t),[0,10π​]

Find the Average Rate of Change of the Function Over $h ( t ) = \sin ( 5 t ) , \left[ 0 , \frac { \pi } { 10 } \right]$