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 2.5.53b
Capitolo 2, Problema 2.5.53b

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\(\right\))=\(\frac{x^2-2x+5}{3x-2}\)

Guida verificata passo dopo passo
1
Identify the function given: \( f(x) = \frac{x^2 - 2x + 5}{3x - 2} \).
Recall that vertical asymptotes occur where the denominator is zero and the numerator is not zero.
Set the denominator equal to zero: \( 3x - 2 = 0 \).
Solve for \( x \) to find the potential vertical asymptote: \( x = \frac{2}{3} \).
Verify that the numerator \( x^2 - 2x + 5 \) is not zero at \( x = \frac{2}{3} \) to confirm the vertical asymptote.

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:
4m

Concetti chiave

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

Vertical Asymptotes

Vertical asymptotes occur in rational functions where the denominator approaches zero while the numerator remains non-zero. These points indicate values of x where the function is undefined, leading to the function's value approaching infinity or negative infinity. To find vertical asymptotes, set the denominator equal to zero and solve for x.
Video consigliato:
Percorso guidato
3:40
Introduction to Cotangent Graph Example 1

Rational Functions

A rational function is a function represented by the ratio of two polynomials. The general form is f(x) = P(x)/Q(x), where P and Q are polynomials. Understanding the behavior of rational functions, particularly their asymptotic behavior, is crucial for analyzing their graphs and identifying points of discontinuity.
Video consigliato:
6:04
Intro to Rational Functions

Finding Roots of Polynomials

Finding the roots of a polynomial involves determining the values of x that make the polynomial equal to zero. This is essential for analyzing rational functions, as the roots of the numerator indicate x-intercepts, while the roots of the denominator help identify vertical asymptotes. Techniques for finding roots include factoring, using the quadratic formula, or applying numerical methods.
Video consigliato:
6:04
Introduction to Polynomial Functions
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

Complete the following steps for the given functions. 


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


f(x)=4x3+4x2+7x+4x2+1f\(\left\)(x\(\right\))=\(\frac{4x^3+4x^2+7x+4}{x^2+1}\)

341
views
Domanda del libro di testo

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)

259
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
Domanda del libro di testo

Determine the following limits.


b. limx→2x−2x5−4x3{\(\displaystyle\)\(\lim\)_{x\(\to\)2}}\(\frac{x-2}{x^5-4x^3}\)

319
views
Domanda del libro di testo

A projectile is fired vertically upward and has a position given by s(t)=−16t^2+128t+192, for 0≤t≤9.


b. From the graph of the position function, identify the time at which the projectile has an instantaneous velocity of zero; call this time t=a.

463
views