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Chapter 4: Q. 54 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

F(x)=x4-16x2-2x

Short Answer

Expert verified

The given rational expression does not have a horizontal or oblique asymptote.

Step by step solution

01

Step 1. Given information

Given rational expression:

F(x)=x4-16x2-2x

02

Step 2. Write the concept

If n鈮�m+2(the degree of the numerator is two or more greater than the degree of the denominator),

the quotient obtained is a polynomial of degree 2 or higher, and R has neither a horizontal nor an oblique

asymptote. In this case, for very large values of x, the graph of R will behave like the graph of the

quotient.

03

Step 3. Calculation

here n=4,m=2

Thus, n鈮�m+2

Therefore no horizontal or oblique asymptote.

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Most popular questions from this chapter

In Problems 63鈥�72, find the real solutions of each equation.

x4-2x3+10x2-18x+9=0

Find the real zeros of f. Use the real zeros to factor f. f(x)=2x3-5x2-4x+12

True or False The graph of a rational function may intersect a vertical asymptote.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.

R(x)=8x2+26x-74x-1

In physics, it is established that the acceleration

due to gravity, g (in meters/sec2), at a height h meters above

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g(h)=3.99脳1014(6.374脳106+h)2

where6.374脳106is the radius of Earth in meters.

(a) What is the acceleration due to gravity at sea level?

(b)

The Willis Tower in Chicago, Illinois, is 443 meters tall.

What is the acceleration due to gravity at the top of the

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(c) The peak of Mount Everest is 8848 meters above sea

level. What is the acceleration due to gravity on the

peak of Mount Everest?

(d) Find the horizontal asymptote of g(h).

(e) Solve g(h)=0. How do you interpret your answer?
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