For the following exercises, use the information in the following table to find h ' ( a ) at the given value for a . x f ( x ) f ' ( x ) g ( x ) g ' ( x ) 0 2 5 0 2 1 1 -2 3 0 2 4 4 1 -1 3 3 -3 2 3 256. [T] The formula for the area of a circle is A = π r 2 , where r is the radius of the circle. Suppose a circle is expanding, meaning that both the area A and the radius r (in inches) are expanding. a. Suppose r = 2 − 100 ( t + 7 ) 2 where t is time in seconds. Use the chain rule d A d t = d A d r ⋅ d r d t to find the rate at which the area is expanding. b. Use a. to find the rate at which the area is expanding t = 4 s
For the following exercises, use the information in the following table to find h ' ( a ) at the given value for a . x f ( x ) f ' ( x ) g ( x ) g ' ( x ) 0 2 5 0 2 1 1 -2 3 0 2 4 4 1 -1 3 3 -3 2 3 256. [T] The formula for the area of a circle is A = π r 2 , where r is the radius of the circle. Suppose a circle is expanding, meaning that both the area A and the radius r (in inches) are expanding. a. Suppose r = 2 − 100 ( t + 7 ) 2 where t is time in seconds. Use the chain rule d A d t = d A d r ⋅ d r d t to find the rate at which the area is expanding. b. Use a. to find the rate at which the area is expanding t = 4 s
For the following exercises, use the information in the following table to find
h
'
(
a
)
at the given value for a.
x
f
(
x
)
f
'
(
x
)
g
(
x
)
g
'
(
x
)
0
2
5
0
2
1
1
-2
3
0
2
4
4
1
-1
3
3
-3
2
3
256. [T] The formula for the area of a circle is
A
=
π
r
2
, where r is the radius of the circle. Suppose a circle is expanding, meaning that both the area A and the radius r (in inches) are expanding.
a. Suppose
r
=
2
−
100
(
t
+
7
)
2
where t is time in seconds. Use the chain rule
d
A
d
t
=
d
A
d
r
⋅
d
r
d
t
to find the rate at which the area is expanding.
b. Use a. to find the rate at which the area is expanding t = 4 s
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