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anonymous
 5 years ago
a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following.
(i) 4 to 5 _______
(ii) 4 to 4.5 _______
(iii) 4 to 4.1 _______
(b) Find the instantaneous rate of change when r = 4.
A'(4) = ______
anonymous
 5 years ago
a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following. (i) 4 to 5 _______ (ii) 4 to 4.5 _______ (iii) 4 to 4.1 _______ (b) Find the instantaneous rate of change when r = 4. A'(4) = ______

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Formula for area: \[A = \pi r^2\] To find average rate of change, find the value of A at both radii and find the difference. i.) \[A _{1}=\pi (4)^2 = 16\pi\] \[A _{2}=\pi (5)^2 = 25\pi\] \[\Delta A = A _2  A _1 = 25\pi  16\pi = 9\pi\] I'll leave ii. and iii. for you to do. For part b  Find dA/dr and let r = 4. \[A = \pi r^2\] \[dA/dr = 2\pi r\] \[dA/dr (4) = 2\pi (4) = 8\pi\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh, whoops. For the average rate of change, you have to divide the change in area by the change in the radius. The first one is (25pi  16pi) / (5  4) = 9pi / 1 = 9pi. This doesn't change the answer for the first one, but you have to remember that for the other two.
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