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Chapter 4: Q. 32 (page 245)

Find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes.

R(x)=x2+3x+2(x+2)2

Short Answer

Expert verified

The domain of the function is x|x≠-2and vertical asymptotes is x=-2 and horizontal asymptote is y=1

Step by step solution

01

Step 1. Given Information

The given function isR(x)=x2+3x+2(x+2)2

02

Step 2. Explanation 

The domain of the function is the set of all real numbers except for all those values for which denominator is 0.

Substitute (x+2)2=0and solve.

(x+2)2=0 x+2=0x=-2

The vertical asymptote is the point at which (x+2)2=0

Thus, the vertical asymptote is x=-2

The horizontal asymptote can be found by dividing the leading coefficients of the numerator and denominator.

Thus, horizontal asymptote is

y=11y=1

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Most popular questions from this chapter

Find the domain of the rational function.

-4x2x-2(x+4)

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

For a rational functionR, if the degree of the numerator is less than the degree of the denominator, then R is ________.

In physics, it is established that the acceleration

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

sea level is given by

g(h)=3.99×1014(6.374×106+h)2

where6.374×106is 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

Willis Tower?

(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?

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 5000cubic inches. See the illustration.

Part (a): Express the surface areaS of the box as a function ofx.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?
See all solutions

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