Question

(4.1) Show, using the $\epsilon - N$ method, that the sequence $a_n = \frac{3n^3 + 2}{n^3}$ converges. First determine the limit.

Name: 41 show using the epsilon n method that the sequence an frac3n3 2n3 converges first determine the limit 44036
Uploaded: 2021-07-27T19:58:22-08:00
Duration: 1 min 2 s
Channel: Tyler Moulton
Description: 41 show using the epsilon n method that the sequence an frac3n3 2n3 converges first determine the limit 44036

          (4.1) Show, using the $\epsilon - N$ method, that the sequence
$a_n = \frac{3n^3 + 2}{n^3}$
converges. First determine the limit.

$41 show using the epsilon n method that the sequence an frac3n3 2n3 converges first determine the limit 44036$

Added by Noah H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Tyler Moulton

07/27/2021

Step 1

The sequence is given by $a_n = \frac{3n^3 + 2}{n^3}$. To find the limit as $n \to \infty$, we can divide both the numerator and the denominator by the highest power of $n$ in the denominator, which is $n^3$. $L = \lim_{n \to \infty} a_n = \lim_{n \to \infty} Show more…

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