Let f(x): = |x-1| x-1 Please follow the same instructions as in #1. 2.(a) f(1) 2.(b) lim f(x) X→-80 2.(c) lim f(x) x→1- 2.(d) lim f(x) 2.(e) lim f(x) x→1 2.(f) lim f(x) x →∞
Let f(x): = |x-1| x-1 Please follow the same instructions as in #1. 2.(a) f(1) 2.(b) lim f(x) X→-80 2.(c) lim f(x) x→1- 2.(d) lim f(x) 2.(e) lim f(x) x→1 2.(f) lim f(x) x →∞
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
Instructions as number 1:
-
Please sketch the graph of f and evaluate each. Use appropriate superscripts.
![### Mathematical Analysis and Limits
**Given Function:**
\[ f(x) = \left| \frac{x-1}{x-1} \right| \]
Please follow the instructions provided earlier in exercise #1.
**Exercises:**
**2(a)** \( f(1) \)
**2(b)** \[ \lim_{x \to -\infty} f(x) \]
**2(c)** \[ \lim_{x \to -1} f(x) \]
**2(d)** \[ \lim_{x \to 1^-} f(x) \]
**2(e)** \[ \lim_{x \to 1^+} f(x) \]
**2(f)** \[ \lim_{x \to \infty} f(x) \]
**Graphical Section:**
There is a section with a graph grid beneath the instructions and exercises. The graph has a standard Cartesian plane layout suitable for plotting functions. This grid can be used to visualize the function \( f(x) \) and analyze the behavior of the limits presented in the exercises.
### Explanation of Graphs and Diagrams:
- **Grid Structure:** The graph grid consists of evenly spaced horizontal and vertical lines, forming square units. This grid assists in plotting the function \( f(x) \) against the x and y-axes. Each square on the grid can be used to represent a certain interval or value, which aids in visualizing how the function behaves near certain points and approaching limits.
- **Axes:** The horizontal axis (x-axis) and the vertical axis (y-axis) should be labeled appropriately based on the variable \( x \) and the function \( f(x) \).
### Instructions for Students:
1. Calculate and evaluate the specified function or limit as per each sub-section from 2(a) to 2(f).
2. Use the provided graph grid to sketch the function and visually confirm your analytical results.
3. Note special points or behaviors such as discontinuities, asymptotic behavior, and specific functional values as \( x \) approaches certain critical points.
This combination of analytical and graphical analysis will deepen your understanding of the behavior of piecewise and absolute value functions, providing a comprehensive approach to analyzing limits and functional values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36f9046e-a34d-43f2-ba4c-c4d16262d63e%2F5eb64b27-f9fc-48c6-a02e-3e3680e705cc%2Fjwvocts_processed.png&w=3840&q=75)
Transcribed Image Text:### Mathematical Analysis and Limits
**Given Function:**
\[ f(x) = \left| \frac{x-1}{x-1} \right| \]
Please follow the instructions provided earlier in exercise #1.
**Exercises:**
**2(a)** \( f(1) \)
**2(b)** \[ \lim_{x \to -\infty} f(x) \]
**2(c)** \[ \lim_{x \to -1} f(x) \]
**2(d)** \[ \lim_{x \to 1^-} f(x) \]
**2(e)** \[ \lim_{x \to 1^+} f(x) \]
**2(f)** \[ \lim_{x \to \infty} f(x) \]
**Graphical Section:**
There is a section with a graph grid beneath the instructions and exercises. The graph has a standard Cartesian plane layout suitable for plotting functions. This grid can be used to visualize the function \( f(x) \) and analyze the behavior of the limits presented in the exercises.
### Explanation of Graphs and Diagrams:
- **Grid Structure:** The graph grid consists of evenly spaced horizontal and vertical lines, forming square units. This grid assists in plotting the function \( f(x) \) against the x and y-axes. Each square on the grid can be used to represent a certain interval or value, which aids in visualizing how the function behaves near certain points and approaching limits.
- **Axes:** The horizontal axis (x-axis) and the vertical axis (y-axis) should be labeled appropriately based on the variable \( x \) and the function \( f(x) \).
### Instructions for Students:
1. Calculate and evaluate the specified function or limit as per each sub-section from 2(a) to 2(f).
2. Use the provided graph grid to sketch the function and visually confirm your analytical results.
3. Note special points or behaviors such as discontinuities, asymptotic behavior, and specific functional values as \( x \) approaches certain critical points.
This combination of analytical and graphical analysis will deepen your understanding of the behavior of piecewise and absolute value functions, providing a comprehensive approach to analyzing limits and functional values.
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 5 steps with 5 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