Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - 11.1 Sequences - 11.1 Exercises: 23

Answer

$\lim\limits_{n \to \infty}$ (3+5n^2)/(n+n^2) $ \lim\limits_{n \to \infty}$ n^2((3/n^2)+5)/n^2((1/n)+1) = (0+5)/(0+1) =5 sequence converges on 5

Work Step by Step

take limit of sequence as n approaches infinity pull out n^2 from both the denominator and numerator cancel out n^2 $ \lim\limits_{n \to \infty}$ (3/n^2) equals 0 because numerator is so small compared to denominator $ \lim\limits_{n \to \infty}$ (1/n) also equals 0 because numerator is so small compared to denominator plug in numbers and solve
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