Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 8: Techniques of Integration - Section 8.8 - Improper Integrals - Exercises 8.8 - Page 501: 8



Work Step by Step

Let $f(r)=\int_{0}^{1} \dfrac{1}{r^{0.999}} dr$ Now, $\lim\limits_{k \to 0^{+}} f(r)= \lim\limits_{k \to 0^{+}}\int_{0}^{1} \dfrac{1}{r^{0.999}} dr$ Thus, $\lim\limits_{k \to 0^{+}} [\dfrac{r^{0.001}}{0.001}]_{1}^{(k)}=\lim\limits_{k \to 0^{+}} [1000-1000(k)^{-0.001}]=1000-0= 1000$
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