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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

The Heaviside function H is defined by

Chapter 1.3, Problem 59E, The Heaviside function H is defined by It is used in the study of electric circuits to represent the

It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on.

(a) Sketch the graph of the Heaviside function.

(b) Sketch the graph of the voltage V(t) in a circuit if the switch is turned on at time t = 0 and 120 volts are applied instantaneously to the circuit. Write a formula for V(t) in terms of H(t).

(c) Sketch the graph or the voltage V(t) in a circuit if the switch is turned on at time t = 5 seconds and 240 volts are applied instantaneously to the circuit. Write a formula for V(t) in terms of H(t). (Note that starting at t = 5 corresponds to a translation.)

(a)

To determine

To sketch: The graph of the Heaviside function.

Explanation

The Heaviside function is, H(t)={0      if t<01

(b)

To determine

To sketch: The graph of V(t) in a circuit if the switch is turned on at time t = 0 and 120 volts are applied to the circuit; write the formula for V(t) in terms of H(t).

(c)

To determine

To sketch: The graph of the voltage in a circuit if the switch is turned on at t = 5 seconds and 240 volts are applied to the circuit; write the formula for V(t) in terms of H(t).

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th