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...
Related questions
Question
![**Question 7 of 20**
**Determine the following limit.**
\[
\lim_{{x \to -\infty}} 6x^{18}
\]
\[
\lim_{{x \to -\infty}} 6x^{18} = \_\_\_
\]
**Explanation:**
This question is asking to find the limit of the function \(6x^{18}\) as \(x\) approaches negative infinity. The expression involves a power of \(x\) raised to the 18th power and multiplied by 6. As \(x\) approaches a very large negative number, the behavior of this polynomial function needs to be determined.
- Since \(x^{18}\) involves an even power, and when raised to an even power, both positive and negative numbers result in a positive value.
- Therefore, as \(x\) approaches negative infinity, \(x^{18}\) continues to grow positively larger.
- Multiplying by 6, a positive constant, the expression \(6x^{18}\) will also approach positive infinity.
Thus, the limit will be positive infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9aba801f-d6d6-46ff-b1fb-9f742e3974df%2Ff96f3900-ddcf-4fba-a545-bf11b112e73a%2Fsleq81_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 7 of 20**
**Determine the following limit.**
\[
\lim_{{x \to -\infty}} 6x^{18}
\]
\[
\lim_{{x \to -\infty}} 6x^{18} = \_\_\_
\]
**Explanation:**
This question is asking to find the limit of the function \(6x^{18}\) as \(x\) approaches negative infinity. The expression involves a power of \(x\) raised to the 18th power and multiplied by 6. As \(x\) approaches a very large negative number, the behavior of this polynomial function needs to be determined.
- Since \(x^{18}\) involves an even power, and when raised to an even power, both positive and negative numbers result in a positive value.
- Therefore, as \(x\) approaches negative infinity, \(x^{18}\) continues to grow positively larger.
- Multiplying by 6, a positive constant, the expression \(6x^{18}\) will also approach positive infinity.
Thus, the limit will be positive infinity.
Expert Solution
Step 1
Here we have to find the limit.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning