Skip to main content
Ch. 2 - Limits
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBriggs 3rd EditionCh. 2 - LimitsProblema 2.4.7c
Capitolo 2, Problema 2.4.7c

The graph of f in the figure has vertical asymptotes at x=1 and x=2. Analyze the following limits. <IMAGE>
lim x→1 f(x)

Guida verificata passo dopo passo
1
Identify the behavior of the function \( f(x) \) as \( x \) approaches 1 from the left (\( x \to 1^- \)).
Identify the behavior of the function \( f(x) \) as \( x \) approaches 1 from the right (\( x \to 1^+ \)).
Determine if the left-hand limit and the right-hand limit as \( x \to 1 \) are equal or not.
If the left-hand limit and right-hand limit are not equal, conclude that the limit \( \lim_{x \to 1} f(x) \) does not exist.
If the left-hand limit and right-hand limit are equal, state that the limit \( \lim_{x \to 1} f(x) \) is equal to that common value.

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:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Vertical Asymptotes

Vertical asymptotes occur in the graph of a function where the function approaches infinity or negative infinity as the input approaches a certain value. In this case, the function f has vertical asymptotes at x=1 and x=2, indicating that as x approaches these values, f(x) does not settle at a finite limit but instead diverges.
Video consigliato:
Percorso guidato
3:40
Introduction to Cotangent Graph Example 1

Limits

A limit describes the behavior of a function as the input approaches a particular value. In the context of vertical asymptotes, the limit of f(x) as x approaches 1 or 2 will help determine whether f(x) approaches positive or negative infinity, which is crucial for understanding the function's behavior near these points.
Video consigliato:
05:50
One-Sided Limits

One-Sided Limits

One-sided limits are used to analyze the behavior of a function as it approaches a specific point from one side only, either the left or the right. For the limits as x approaches 1, it is important to evaluate both the left-hand limit (as x approaches 1 from values less than 1) and the right-hand limit (as x approaches 1 from values greater than 1) to fully understand the function's behavior at the asymptote.
Video consigliato:
05:50
One-Sided Limits
Pratica correlata
Domanda del libro di testo

For the following position functions, make a table of average velocities similar to those in Exercises 19–20 and make a conjecture about the instantaneous velocity at the indicated time. 


c. s(t)=40 sin 2t at t=0

370
views
Domanda del libro di testo

Determine whether the following statements are true and give an explanation or counterexample.


c. The graph of a function can have any number of vertical asymptotes but at most two horizontal asymptotes.

393
views
Domanda del libro di testo

Complete the following steps for the given functions. 


c. Graph f and all of its asymptotes with a graphing utility. Then sketch a graph of the function by hand, correcting any errors appearing in the computer-generated graph.


f(x)=x2−2x+53x−2f\(\left\)(x\(\right\))=\(\frac{x^2-2x+5}{3x-2}\)

328
views
Domanda del libro di testo

Complete the following steps for the given functions. 


b. Find the vertical asymptotes of ff (if any).


f(x)=x2−2x+53x−2f\(\left\)(x\(\right\))=\(\frac{x^2-2x+5}{3x-2}\)

363
views
Domanda del libro di testo

The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>

lim x→−2 h(x)

208
views
Domanda del libro di testo

Complete the following steps for the given functions. 


c. Graph f and all of its asymptotes with a graphing utility. Then sketch a graph of the function by hand, correcting any errors appearing in the computer-generated graph.


f(x)=3x2−2x+53x+4f\(\left\)(x\(\right\))=\(\frac{3x^2-2x+5}{3x+4}\)

234
views