Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.2 - Exponents and Radicals - 1.2 Exercises - Page 25: 107

Answer

As the $n$ gets large in the $n$th root of 2, the result will reach 1 from above As the $n$ gets large in the $n$th root of $\frac{1}{2}$, the result will reach 1 from below As $n$ gets large in the equation of $n^{1/n}$ the number will reach 1 from above

Work Step by Step

$2^{1/1}=2$, $2^{1/2}=1.4142$, $2^{1/5}=1.148698$, $2^{1/10}=1.07177$, $2^{1/100}=1.00696$ $(1/2)^{1/1}=0.5$, $(1/2)^{1/2}=0.70711$, $(1/2)^{1/5}=0.87055$, $(1/2)^{1/10}=0.93303$, $(1/2)^{1/100}=0.99309$ $1^{1/1}=1$, $2^{1/2}=1.41421$, $5^{1/5}=1.37973$, $10^{1/10}=1.25893$, $100^{1/100}=1.04713$
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