University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.1 - Functions and Their Graphs - Exercises - Page 12: 32

Answer

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Work Step by Step

$a).$ Find the equation of line that goes through the points $\ (0,0)\ \ \mathrm{and}\ \ (\frac{T}{2},0)\ $ and the line that goes through $\ (\frac{T}{2},0)\ \ \mathrm{and}\ \ (0,1).$ Secondly, write down the domain restrictions. $\mathrm{First\:part:}$ Equation of the horizontal line is $\ y=0\ $ on $\ [0,\frac{T}{2}].$ $\mathrm{Second\:part:}$ $y-0=\frac{1-0}{T-\frac{T}{2}}(x-\frac{T}{2})$ $y=\frac{2}{T}x-1\ \ $ on $\ \ (\frac{T}{2},T]$ $b).$ Equation of the horizontal lines are $\ y=-A\ $ and $\ y=A\ $. Find the domain restrictions. $y=-A\ \ $ on $\ \ [\frac{T}{2},T)\ \ and\ \ [\frac{3}{2}T,2T].$ $y=A\ \ $ on $\ \ [0,\frac{T}{2})\ \ and\ \ [T,\frac{3}{2}T).$
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