Question

section 3.7
score: 4/10 answered: 4/10
question 5
find the horizontal asymptote of ( f(x)=\frac{x + 3x^{3}+4}{2x^{3}-x^{2}-5} )
( y= )
question help: video

Explanation:

Step1: Identify the degrees of numerator and denominator

The degree of the numerator \(n = 3\) (from \(3x^{3}\)), and the degree of the denominator \(m=3\) (from \(2x^{3}\)).

Step2: Use the rule for horizontal asymptote when \(n = m\)

When \(n = m\), the horizontal asymptote \(y=\frac{\text{leading coefficient of numerator}}{\text{leading coefficient of denominator}}\).
The leading coefficient of the numerator is \(3\), and the leading coefficient of the denominator is \(2\). So \(y = \frac{3}{2}\).

Answer:

\(y=\frac{3}{2}\)