Domanda del libro di testo
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
c. limx→0− f(x) = 0
300
views
Ch. 2 - Limits and Continuity
Hass15th EditionThomas' CalculusISBN: 9780137616077
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions490
- Ch. 8 - Techniques of Integration399
- Ch. 9 - First-Order Differential Equations66
- Ch. 10 - Infinite Sequences and Series132
- Ch. 11 - Parametric Equations and Polar Coordinates58
Capitolo 2, Problema 1a
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
a. limx→−1+ f(x) = 1
Guida verificata passo dopo passo1
Examine the graph of the function y = f(x) as x approaches -1 from the right (x → -1+). This means you should look at the values of f(x) as x gets closer to -1 from values greater than -1.
Identify the y-value that the function approaches as x approaches -1 from the right. This is the value of the right-hand limit, limx→−1+ f(x).
Check if the y-value that the function approaches as x approaches -1 from the right is equal to 1.
If the y-value is equal to 1, then the statement limx→−1+ f(x) = 1 is true. Otherwise, it is false.
Conclude whether the statement is true or false based on the y-value identified in the previous steps.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Limits
A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It helps in understanding how functions behave near points of interest, including points of discontinuity. For example, limx→−1+ f(x) refers to the limit of f(x) as x approaches -1 from the right side.
Video consigliato:
05:50
One-Sided Limits
One-Sided Limits
One-sided limits are limits that consider the behavior of a function as the input approaches a specific value from one direction only. The notation limx→−1+ f(x) indicates the limit as x approaches -1 from the right (values greater than -1). This is crucial for analyzing functions that may behave differently from the left and right at a point.
Video consigliato:
05:50One-Sided Limits
Graphical Interpretation of Limits
Graphical interpretation of limits involves analyzing the graph of a function to determine the value that the function approaches as the input approaches a certain point. By observing the graph near x = -1, one can visually assess whether the function approaches a specific value, which aids in confirming or refuting statements about limits.
Video consigliato:
6:47Finding Limits Numerically and Graphically
Pratica correlata
Domanda del libro di testo
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
f. limx→0 f(x) = 0
343
views
Domanda del libro di testo
Finding Limits Graphically
Which of the following statements about the function y = f(x) graphed here are true, and which are false?
e. limx→0 f(x) exists
324
views