Homework Help is Here – Start Your Trial Now!
Math
Calculus
1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ H-3- I-3 f(x) = { 2 -x+4 x - 3 x <3 I 23

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question
Hi! I need these solved for this graph. A. f(-2) B. Lim f(x) X------>-2 C. f(0) D. Lim f(x) X------>0 E. f(2) F. Lim f(x) X------>2 G. f(4) H. Lim f(x) X-------->4 Graph: Also included these two other problems on this other image. Please answer them all so i can up vote your answer. Thanks everyone.
Certainly! Below is the transcription and detailed explanation of the graph for an educational website. --- ### Understanding Graphical Representation of Functions #### Graph Description The graph displayed on this page represents a mathematical function depicted in the Cartesian coordinate system with the x-axis (horizontal) and y-axis (vertical). - The x-axis ranges from -2 to 5. - The y-axis ranges from -2 to 4. #### Key Features of the Graph 1. **Axes and Scale**: - The x-axis is labeled with values from -2 to 5. - The y-axis is labeled with values from -2 to 4. - Both axes intersect at the origin (0,0). 2. **Graph Behavior**: - There is a vertical asymptote at \( x = -2 \). - The function decreases towards negative infinity as it approaches \( x = -2 \) from the right. - At \( x = 0 \) and \( x = 2 \), there are open circles indicating discontinuities in the function. - The function value at \( x = 0 \) is approaching 2 from the left and right. - The function decreases to a minimum at \( x = 2 \) and then increases again, forming a valley shape. - At \( x = 4 \), the function has a closed circle hovering at \( y = 3.5 \). 3. **General Shape**: - The graph shows peaks and valleys, indicating it is not a linear function. - The leftmost part of the graph starts at the top moving downwards steeply. - After the drop past \( x = -2 \), the graph increases steeply, moving through a valley. - Finally, there is a sharp increase with another steep incline starting from just before \( x = 5 \). 4. **Discontinuities**: - There are distinct points of discontinuity at \( x = 0 \) and \( x = 2 \) where the function has open circles. - The value of the function at \( x = 4 \) extends with an open circle indicating a defined y-value for that x-coordinate. #### Summary This graph displays multiple characteristics such as asymptotes, discontinuities, and varying slopes. Understanding these elements helps in grasping the behavior of complex functions, particularly in evaluating limits and continuity. Evaluating such functions
Transcribed Image Text:Certainly! Below is the transcription and detailed explanation of the graph for an educational website. --- ### Understanding Graphical Representation of Functions #### Graph Description The graph displayed on this page represents a mathematical function depicted in the Cartesian coordinate system with the x-axis (horizontal) and y-axis (vertical). - The x-axis ranges from -2 to 5. - The y-axis ranges from -2 to 4. #### Key Features of the Graph 1. **Axes and Scale**: - The x-axis is labeled with values from -2 to 5. - The y-axis is labeled with values from -2 to 4. - Both axes intersect at the origin (0,0). 2. **Graph Behavior**: - There is a vertical asymptote at \( x = -2 \). - The function decreases towards negative infinity as it approaches \( x = -2 \) from the right. - At \( x = 0 \) and \( x = 2 \), there are open circles indicating discontinuities in the function. - The function value at \( x = 0 \) is approaching 2 from the left and right. - The function decreases to a minimum at \( x = 2 \) and then increases again, forming a valley shape. - At \( x = 4 \), the function has a closed circle hovering at \( y = 3.5 \). 3. **General Shape**: - The graph shows peaks and valleys, indicating it is not a linear function. - The leftmost part of the graph starts at the top moving downwards steeply. - After the drop past \( x = -2 \), the graph increases steeply, moving through a valley. - Finally, there is a sharp increase with another steep incline starting from just before \( x = 5 \). 4. **Discontinuities**: - There are distinct points of discontinuity at \( x = 0 \) and \( x = 2 \) where the function has open circles. - The value of the function at \( x = 4 \) extends with an open circle indicating a defined y-value for that x-coordinate. #### Summary This graph displays multiple characteristics such as asymptotes, discontinuities, and varying slopes. Understanding these elements helps in grasping the behavior of complex functions, particularly in evaluating limits and continuity. Evaluating such functions
### Calculus Problems: Limits and Continuity #### 1. Evaluate the limits of \( f(x) \) as \( x \) approaches 3 from the left, as \( x \) approaches 3, and as \( x \) approaches 3 from the right for the following function: Given: \[ f(x) = \begin{cases} -x + 4 & \text{if } x < 3 \\ x - 3 & \text{if } x \geq 3 \end{cases} \] **Tasks:** \[ \lim_{x \to 3^-} f(x), \quad \lim_{x \to 3} f(x), \quad \lim_{x \to 3^+} f(x) \] --- #### 2. (Task 2 is unspecified in the image and should be filled based on context or instructor's direction.) --- #### 3. Determine whether the function is continuous at \( x = 5 \): Given: \[ f(x) = \begin{cases} \frac{x^2 - 4x - 5}{x - 5} & \text{if } x < 5 \\ x + 2 & \text{if } x \geq 5 \end{cases} \] **Tasks:** Check the continuity of \( f(x) \) at \( x = 5 \).
Transcribed Image Text:### Calculus Problems: Limits and Continuity #### 1. Evaluate the limits of \( f(x) \) as \( x \) approaches 3 from the left, as \( x \) approaches 3, and as \( x \) approaches 3 from the right for the following function: Given: \[ f(x) = \begin{cases} -x + 4 & \text{if } x < 3 \\ x - 3 & \text{if } x \geq 3 \end{cases} \] **Tasks:** \[ \lim_{x \to 3^-} f(x), \quad \lim_{x \to 3} f(x), \quad \lim_{x \to 3^+} f(x) \] --- #### 2. (Task 2 is unspecified in the image and should be filled based on context or instructor's direction.) --- #### 3. Determine whether the function is continuous at \( x = 5 \): Given: \[ f(x) = \begin{cases} \frac{x^2 - 4x - 5}{x - 5} & \text{if } x < 5 \\ x + 2 & \text{if } x \geq 5 \end{cases} \] **Tasks:** Check the continuity of \( f(x) \) at \( x = 5 \).
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS