Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Section 1.3 - New Functions from Old Functions - 1.3 Exercises - Page 45: 64

Answer

(a) $tH(t) = 0~~~~~$ if $t \lt 0$ $tH(t) = t~~~~~$ if $t \geq 0$ We can see a sketch of the graph $y = tH(t)$ below. (b) $V(t) = 2tH(t)$ We can see a sketch of the graph below. (c) $V(t) = 4(t-7)H(t-7)$ We can see a sketch of the graph below.

Work Step by Step

(a) $tH(t) = 0~~~~~$ if $t \lt 0$ $tH(t) = t~~~~~$ if $t \geq 0$ We can see a sketch of the graph $y = tH(t)$ below. (b) If the voltage is gradually turned on and reaches a level of 120 V in a time of 60 seconds, then $c=2$ in the ramp function. $V(t) = 2tH(t)$ We can see a sketch of the graph below. (c) If the voltage is gradually turned on and reaches a level of 100 V in a time of 25 seconds, then $c=4$ in the ramp function. We also need to include $(t-7)$ to account for the 7 second delay. Thus the graph is shifted horizontally to the right by 7 units. $V(t) = 4(t-7)H(t-7)$ We can see a sketch of the graph below.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.