Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises: 39

Answer

(a) $$A(2)=2\cdot6=12.$$ (b) $$A(6)=6\cdot6=36.$$ (c) $$A(x)=x\cdot6=6x.$$

Work Step by Step

(a) Here we just get the rectangle bounded by $y=6$, $y=0$ (the $t$ axis), $t=0$ (the $y$ axis) and $t=2$. So the sides of this rectangle are $a=6$ (height) and $b=2$ (width) so the area is $$A(2)=2\cdot6=12.$$ (b) Here we just get the rectangle bounded by $y=6$, $y=0$ (the $t$ axis), $t=0$ (the $y$ axis) and $t=6$. So the sides of this rectangle are $a=6$ (height) and $b=6$ (width) so the area is $$A(6)=6\cdot6=36.$$ (c) Here we just get the rectangle bounded by $y=6$, $y=0$ (the $t$ axis), $t=0$ (the $y$ axis) and $t=x$. So the sides of this rectangle are $a=6$ (height) and $b=x$ (width) so the area is $$A(x)=x\cdot6=6x.$$
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