28 Oct 2021
Problem 13c
Page 238
Section 3.8: Rates of Change in the Natural and Social Sciences
Chapter 3: Differentiation Rules
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28 Oct 2021
Given information
Given to show that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the circumference of the circle. Also, explain it graphically and describe a method to detail the change in the area when the change in radius is smaill.
Step-by-step explanation
Step 1.
Use the formula of the area of a circle to explain the first part of the question.
Finding the derivative of the rate of change so, differentiate the area with respect to time
Thus, is the circumference of the circle.
Hence, it is verified that the rate of change of the area of a circle with respect to its radius (at any ) is equal to the circumference of the circle.