Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

APPENDIX E - Sigma Notation - E Exercises: 10

Answer

$f(x_{1})\triangle x_{1}+f(x_{2})\triangle x_{2}+f(x_{3})\triangle x_{3}+f(x_{4})\triangle x_{4}+\cdots+f(x_{n})\triangle x_{n}$

Work Step by Step

We expand the sigma notation by writing $f(x_{i})\triangle x_{i}$ as $i$ increases from 1 to n: $\displaystyle \sum_{i=1}^{n}f(x_{i})\triangle x_{i}=f(x_{1})\triangle x_{1}+f(x_{2})\triangle x_{2}+f(x_{3})\triangle x_{3}+f(x_{4})\triangle x_{4}+\cdots+f(x_{n})\triangle x_{n}$
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