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 2.5.56b
Capitolo 2, Problema 2.5.56b

Complete the following steps for the given functions. 


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


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

Guida verificata passo dopo passo
1
Identify the vertical asymptotes by finding the values of x that make the denominator zero.
Set the denominator equal to zero: 3x + 4 = 0.
Solve the equation for x: 3x = -4.
Divide both sides by 3 to isolate x: x = -\(\frac{4}{3}\).
Conclude that the vertical asymptote is at x = -\(\frac{4}{3}\).

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 does not. These points indicate where the function's value tends to infinity or negative infinity. To find vertical asymptotes, set the denominator equal to zero and solve for the variable, ensuring that the numerator does not also equal zero at those points.
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

Polynomial Functions

Polynomial functions are expressions that consist of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. The degree of a polynomial indicates its highest power, which influences its end behavior and the number of roots it can have. In the context of rational functions, the behavior of the numerator polynomial is essential for determining limits and asymptotic behavior.
Video consigliato:
6:04
Introduction to Polynomial Functions
Pratica correlata
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

Assume you invest \$250 at the end of each year for 10 years at an annual interest rate of rr. The amount of money in your account after 10 years is given by A(r)=250((1+r)10−1)rA\left(r\right)=\frac{250\left(\left(1+r\right)^{10}-1\right)}{r}. Assume your goal is to have \$3500 in your account after 10 years.


b. Use a calculator to estimate the interest rate required to reach your financial goal.

398
views
Domanda del libro di testo

Graph the function f(x)=e^−x / x(x+2)^2 using a graphing utility. (Experiment with your choice of a graphing window.) Use your graph to determine the following limits.


b. lim x→−2 f(x)

234
views
Domanda del libro di testo

Complete the following sentences in terms of a limit.


b. A function is continuous from the right at a if _____ .

248
views
Domanda del libro di testo

Use the graph of gg in the figure to find the following values or state that they do not exist. <IMAGE>

limx→0g(x){\(\displaystyle\)\(\lim\)_{x\(\to\)0}g\(\left\)(x\(\right\))}

389
views
Domanda del libro di testo

Determine the following limits.


b. limx→3x−3x4−9x2{\(\displaystyle\)\(\lim\)_{x\(\to\)3}}\(\frac{x-3}{x^4-9x^2}\)

322
views