Problem

Let $ f $ and $ g $ be linear functions with equa…

01:23

Problem 60 Hard Difficulty

The Heaviside function defined in Exercise 59 can also be used to define the ramp function $ y = ctH(t) $ , which represents a gradual increase in voltage or current in a circuit.

(a) Sketch the graph of the ramp function $ y = tH(t) $.
(b) Sketch the graph of the voltage $ V(t) $ in a circuit if the switch is turned on at time $ t = 0 $ and the voltage is gradually increased to 120 volts over a 60-second time interval. Write a formula for $ V(t) $ in terms of $ H(t) $ for $ t \le 60 $.
(c) Sketch the graph of the voltage $ V(t) $ in a circuit if the switch is turned on at time $ t = 7 $ seconds and the voltage is gradually increased to 100 volts over a period of 25 seconds. Write a formula for $ V(t) $ in terms of $ H(t) $ for $ t \le 32 $.

Answer

a) see step for solution
b) $V(t)=2 t H(t)$
c) $V(t)=4(t-7) H(t-7)$

More Answers

04:43

Clarissa N.

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Discussion

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Tuv D.

August 16, 2020

Part c), when t=7, V(7)=0, so the slope of the graph should be from 0 to 100 for [7,32]

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Video Transcript

So for the given problem um we can use it to define the ramp function Y equals C. T. Hft. Um Which is going to represent a gradual increase in the voltage or current in a circuit. So we're going to sketch the graph of the ramp function. We see the voltage is going to be in this case C is going to be too so we'll have to t 3 50. And then given the ramp function we'll eventually end up getting um Since this is Changing turned on at seven seconds we'll have four Times T -7 yeah. of eight times at age 15 and seven. So that will be our final uh resulting function for the voltage.

Carson M.

California Baptist University

Topics

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Top Calculus 3 Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Michael J.

Idaho State University

Joseph L.

Boston College