Mathematics, 27.04.2021 22:10 drainy0uandthefish
Use the difference quotient of A(r)= πr2 to calculate the average rate of change during certain intervals.
The difference quotient of A(r) is:
StartFraction pi (r + h) squared minus pi r squared Over h EndFraction = StartFraction pi (r squared + 2 r h + h squared) minus pi r squared Over h EndFraction = StartFraction pi r squared + 2 pi r h + pi h squared minus pi r squared Over h EndFraction = 2 pi r + pi h
The average rate of change from the interval 2 to 3 inches is
π square inches per inch.
The average rate of change from the interval 2 to 2.5 is
π square inches per inch.
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