Homework Help is Here – Start Your Trial Now!
Math
Calculus
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negativ infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". lim 4 n 8n

Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negativ infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". lim 4 n 8n

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". 2,4 lim n→∞ e8n
Transcribed Image Text:Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "oo" (without the quotation marks). If it diverges to negative infinity, state your answer as "-oo". If it diverges without being infinity or negative infinity, state your answer as "DNE". 2,4 lim n→∞ e8n
Expert Solution
Step 1

NOTE: Refresh your page if you can't see any equations.

.

find the given limit

\lim _{n\to \infty }\left(\frac{n^4}{e^{8n}}\right)

use L'hospital's rule

=\lim _{n\to \infty }\left(\frac{\frac{d}{dn}\left(n^4\right)}{\frac{d}{dn}\left(e^{8n}\right)}\right)

=\lim _{n\to \infty }\left(\frac{4n^3}{8\cdot e^{8n}}\right)

=\lim _{n\to \infty }\left(\frac{n^3}{2e^{8n}}\right)

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 23 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS