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
![Below is the transcription and detailed description:
## Question
Which of the following vectors represents the correct expression?
### Options:
1. \[
\left\langle \frac{1}{\sqrt{1 + t^2}}, \, \frac{1}{t^2 \sqrt{1 + t^{-2}}} \right\rangle
\]
2. \[
\left\langle \frac{1}{\sqrt{1 + t^{-4}}}, \, \frac{1}{t \sqrt{1 + t^{-4}}} \right\rangle
\]
3. \[
\left\langle \frac{1}{\sqrt{1 + t^{-4}}}, \, \frac{1}{t^2 \sqrt{1 + t^{-4}}} \right\rangle
\]
4. \[
\left\langle \frac{1}{\sqrt{1 + t^{-2}}}, \, \frac{1}{t \sqrt{1 + t^{-2}}} \right\rangle
\]
### Explanation:
Each option consists of a vector represented in the form \(\left\langle f(t), g(t) \right\rangle\), where \(f(t)\) and \(g(t)\) are functions of the variable \(t\).
- For the first option, the components are \(\frac{1}{\sqrt{1 + t^2}}\) and \(\frac{1}{t^2 \sqrt{1 + t^{-2}}}\).
- For the second option, the components are \(\frac{1}{\sqrt{1 + t^{-4}}}\) and \(\frac{1}{t \sqrt{1 + t^{-4}}}\).
- For the third option, the components are \(\frac{1}{\sqrt{1 + t^{-4}}}\) and \(\frac{1}{t^2 \sqrt{1 + t^{-4}}}\).
- For the fourth option, the components are \(\frac{1}{\sqrt{1 + t^{-2}}}\) and \(\frac{1}{t \sqrt{1 + t^{-2}}}\).
The selected option is indicated with a dark filled circle next to it. The correct option marked here is:
\[
\left\langle \frac{1}{\sqrt{1 + t^{-4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde5535f4-bfc5-4672-a20d-4797632e4aa9%2F4c1f26ba-70fd-4ed1-bcdd-5b07d55ca75f%2Fosuprwp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Below is the transcription and detailed description:
## Question
Which of the following vectors represents the correct expression?
### Options:
1. \[
\left\langle \frac{1}{\sqrt{1 + t^2}}, \, \frac{1}{t^2 \sqrt{1 + t^{-2}}} \right\rangle
\]
2. \[
\left\langle \frac{1}{\sqrt{1 + t^{-4}}}, \, \frac{1}{t \sqrt{1 + t^{-4}}} \right\rangle
\]
3. \[
\left\langle \frac{1}{\sqrt{1 + t^{-4}}}, \, \frac{1}{t^2 \sqrt{1 + t^{-4}}} \right\rangle
\]
4. \[
\left\langle \frac{1}{\sqrt{1 + t^{-2}}}, \, \frac{1}{t \sqrt{1 + t^{-2}}} \right\rangle
\]
### Explanation:
Each option consists of a vector represented in the form \(\left\langle f(t), g(t) \right\rangle\), where \(f(t)\) and \(g(t)\) are functions of the variable \(t\).
- For the first option, the components are \(\frac{1}{\sqrt{1 + t^2}}\) and \(\frac{1}{t^2 \sqrt{1 + t^{-2}}}\).
- For the second option, the components are \(\frac{1}{\sqrt{1 + t^{-4}}}\) and \(\frac{1}{t \sqrt{1 + t^{-4}}}\).
- For the third option, the components are \(\frac{1}{\sqrt{1 + t^{-4}}}\) and \(\frac{1}{t^2 \sqrt{1 + t^{-4}}}\).
- For the fourth option, the components are \(\frac{1}{\sqrt{1 + t^{-2}}}\) and \(\frac{1}{t \sqrt{1 + t^{-2}}}\).
The selected option is indicated with a dark filled circle next to it. The correct option marked here is:
\[
\left\langle \frac{1}{\sqrt{1 + t^{-4
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 2 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