The average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].
What is the average rate of change?
The average Rate of Change of the function f(x) can be calculated as;
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]
The given function is f(x) = 2sin(1/2)x on the interval [0, π]
Here a = 0
b = π
f(a) = 2sin(1/2)a
f(0) = 0
f(b) = 2sin(1/2)π = 2
Step 2: Find Average
[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}\\\\f(x) = \dfrac{2- 0}{\pi }\\\\f(x) = \dfrac{2}{\pi }\\[/tex]
Therefore, the average rate of change of the function in the given interval [0, π] is [tex]\dfrac{2}{\pi }[/tex].
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