The level of water h in a water clock is governed by the equation dh dt -h/3 • Sketch the slope field in the upper half-plane h > 0.

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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dh
The level of water h in a water clock is governed by the equation
dt
= -h!/3
• Sketch the slope field in the upper half-plane h > 0.
• Use Separation of Variables to find a solution in the domain (-0, 1] with h(1) = 0.
• Prove that the function
your solution to (b),t < 1,
0, t > 1
h(t)
is differentiable and satisfies the differential equation. Draw the corresponding solution curve on your picture for (a).
Note that the solution in the last part makes sense in terms of water clock.
Transcribed Image Text:dh The level of water h in a water clock is governed by the equation dt = -h!/3 • Sketch the slope field in the upper half-plane h > 0. • Use Separation of Variables to find a solution in the domain (-0, 1] with h(1) = 0. • Prove that the function your solution to (b),t < 1, 0, t > 1 h(t) is differentiable and satisfies the differential equation. Draw the corresponding solution curve on your picture for (a). Note that the solution in the last part makes sense in terms of water clock.
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