Find the limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim (ex + 7 cos(4x)) x → 00
Find the limit. (If the limit is infinite, enter 'co' or '-co', as appropriate. If the limit does not otherwise exist, enter DNE.) lim (ex + 7 cos(4x)) x → 00
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...
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**Problem Statement:** Find the limit. (If the limit is infinite, enter 'oo' or '-oo', as appropriate. If the limit does not otherwise exist, enter DNE.)
**Mathematical Expression:**
\[
\lim_{{x \to \infty}} \left( e^{-x} + 7 \cos(4x) \right)
\]
**Answer Box:**
[ ]
---
In this problem, you're tasked with finding the limit of the function as \( x \) approaches infinity. The function includes an exponential term \( e^{-x} \) and a cosine term \( 7 \cos(4x) \).
When evaluating this limit:
1. The term \( e^{-x} \) approaches 0 as \( x \) approaches infinity because the exponential function decays rapidly.
2. The cosine term, \( 7 \cos(4x) \), oscillates between -7 and 7 with a constant amplitude.
To find the limit, consider these behaviors as \( x \) grows indefinitely.
If you have questions or need further assistance, please reach out to your instructor or refer to your textbook's section on limits and oscillatory functions.
Happy Studying!
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e135d5c-f867-4afd-9f0d-b505f4f19664%2F5092cb46-d7ad-49a3-a473-b8faa1759524%2Fgy346ok_processed.png&w=3840&q=75)
Transcribed Image Text:---
**Problem Statement:** Find the limit. (If the limit is infinite, enter 'oo' or '-oo', as appropriate. If the limit does not otherwise exist, enter DNE.)
**Mathematical Expression:**
\[
\lim_{{x \to \infty}} \left( e^{-x} + 7 \cos(4x) \right)
\]
**Answer Box:**
[ ]
---
In this problem, you're tasked with finding the limit of the function as \( x \) approaches infinity. The function includes an exponential term \( e^{-x} \) and a cosine term \( 7 \cos(4x) \).
When evaluating this limit:
1. The term \( e^{-x} \) approaches 0 as \( x \) approaches infinity because the exponential function decays rapidly.
2. The cosine term, \( 7 \cos(4x) \), oscillates between -7 and 7 with a constant amplitude.
To find the limit, consider these behaviors as \( x \) grows indefinitely.
If you have questions or need further assistance, please reach out to your instructor or refer to your textbook's section on limits and oscillatory functions.
Happy Studying!
---
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