86. If you drop a pebble into a large lake, you will cause a cir- cle of ripples to expand outward. The area A = A(t) and radius r= r(t) are clearly functions of t (they change over time) and are related by the formula A = ar?. Area A = A(t) r = r(t) t, seconds (a) If r is measured in inches and t is measured in seconds, what are the units of ? What are the units dt of dr dA and explain the practical meaning of (b) Find dr dA dr r=2 dA (c) Find and explain the practical meaning of dt dA| dt \r=2

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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86. If you drop a pebble into a large lake, you will cause a cir-
cle of ripples to expand outward. The area A = A(t) and
radius r= r(t) are clearly functions of t (they change over
time) and are related by the formula A = ar?.
Area A = A(t)
r = r(t)
t, seconds
(a) If r is measured in inches and t is measured in
seconds, what are the units of ? What are the units
dt
of
dr
dA
and explain the practical meaning of
(b) Find
dr
dA
dr r=2
dA
(c) Find
and explain the practical meaning of
dt
dA|
dt \r=2
Transcribed Image Text:86. If you drop a pebble into a large lake, you will cause a cir- cle of ripples to expand outward. The area A = A(t) and radius r= r(t) are clearly functions of t (they change over time) and are related by the formula A = ar?. Area A = A(t) r = r(t) t, seconds (a) If r is measured in inches and t is measured in seconds, what are the units of ? What are the units dt of dr dA and explain the practical meaning of (b) Find dr dA dr r=2 dA (c) Find and explain the practical meaning of dt dA| dt \r=2
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