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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 71E
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

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage