Skip to main content
Ch. 2 - Limits and Continuity
Hass - Thomas' Calculus 15th Edition
Hass15th EditionThomas' CalculusISBN: 9780137616077Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoHass 15th EditionCh. 2 - Limits and ContinuityProblema 1f
Capitolo 2, Problema 1f

Finding Limits Graphically


Which of the following statements about the function y = f(x) graphed here are true, and which are false?


img


f. limx→0 f(x) = 0

Guida verificata passo dopo passo
1
To determine the limit of f(x) as x approaches 0, examine the graph of the function y = f(x) near x = 0.
Observe the behavior of the function values (y-values) as x gets closer to 0 from both the left and the right sides.
If the y-values approach a single, specific value as x approaches 0 from both directions, then the limit exists and is equal to that value.
If the y-values from the left and right do not approach the same value, then the limit does not exist.
Based on the graph, determine if the y-values approach 0 as x approaches 0 from both sides to conclude if lim(x→0) f(x) = 0 is true or false.

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:
3m

Concetti 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 the value that a function approaches, even if it does not actually reach that value. For example, limx→0 f(x) = 0 means that as x gets closer to 0, the function f(x) approaches 0.
Video consigliato:
05:50
One-Sided Limits

Graphical Interpretation of Limits

Graphically, limits can be analyzed by observing the behavior of a function's graph near a specific point. If the graph approaches a particular y-value as x approaches a certain x-value, that y-value is the limit. This visual approach is crucial for determining the truth of statements about limits based on the graph provided.
Video consigliato:
6:47
Finding Limits Numerically and Graphically

Continuity

A function is continuous at a point if the limit as x approaches that point equals the function's value at that point. This means there are no breaks, jumps, or holes in the graph at that point. Understanding continuity is essential for evaluating limits, as it helps determine whether the limit can be directly substituted into the function.
Video consigliato:
05:34
Intro to Continuity
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?



a. limx→−1+ f(x) = 1

294
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?



c. limx→0− f(x) = 0

300
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?



j. limx→2− f(x) = 2

268
views
Domanda del libro di testo

Limits of quotients


Find the limits in Exercises 23–42.


limx→−3 (2 − √(x² − 5)) / (x + 3)

197
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
Domanda del libro di testo

[Technology Exercise] 22. Make a table of values for the function at the points x=1.2, x=11/10, x=101/100, x=1001/1000, x=10001/10000, and x = 1.

         

a. Find the average rate of change of F(x) over the intervals [1,x] for each x≠1 in your table.

         

b. Extending the table if necessary, try to determine the rate of change of F(x) at x = 1.

335
views