Chapter 4: Q. 49 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$Q (x) = \frac{2 x^{2} - 5 x - 12}{3 x^{2} - 11 x - 4}$

Short Answer

Expert verified

$y = \frac{2}{3}$ will be the horizontal asymptote for given rational expression.

Step by step solution

Step 1. Given information

Given rational expression:

$Q (x) = \frac{2 x^{2} - 5 x - 12}{3 x^{2} - 11 x - 4}$

Step 2. Write the concept

If n = m (the degree of the numerator equals the degree of the denominator), the quotient obtained will be

the number $\frac{a_{n}}{b_{m}}$ , and the line $y = \frac{a_{n}}{b_{m}}$ is a horizontal asymptote.

Step 3. Calculation

Here, $n = 2, m = 2$

Now

$F (x) = \frac{2 x^{2} - 5 x - 12}{3 x^{2} - 11 x - 4} T a k i n g x^{2} c o m m o n f r o m n u m e r a t o r a n d d e n o m i n a t o r w e g e t = l i m_{x \to \infty} \frac{x^{2} (2 - \frac{5 x}{x^{2} - \frac{12}{x^{2}})}}{x^{2} (3 - \frac{11 x}{x^{2} - \frac{4}{x^{2}})}} = \frac{2}{3} i . e \frac{a_{n}}{b_{m}} = \frac{2}{3}$

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$Q (x) = \frac{2 x^{2} - 5 x - 12}{3 x^{2} - 11 x - 4}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.Q(x)=2x2-5x-123x2-11x-4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Applied Mathematics

Statistics

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$Q (x) = \frac{2 x^{2} - 5 x - 12}{3 x^{2} - 11 x - 4}$