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Chapter 14: Q. 87 (page 890)

For Problems 83 鈥� 88, use a graphing utility to graph the functions R given in Problems 77鈥� 82. Verify the solutions found above.

R(x)=x3+2x2+xx4+x3+2x+2

Short Answer

Expert verified

Using the graphing utility the asymptotes and holes of the function R(x)=x3+2x2+xx4+x3+2x+2are verified.

Step by step solution

01

Step 1. Given Information

We are given a rational function R(x)=x3+2x2+xx4+x3+2x+2.

We need to use a graphing utility and verify the asymptotes and holes of the function.

02

Step 2. Graph the function and verify the result

The graph of the function R(x)=x3+2x2+xx4+x3+2x+2is given as

It can be seen that the graph is discontinuous at two points. At x=-23there is a vertical asymptote and at x=-1there is a hole at -1,0.

So the results are verified.

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Most popular questions from this chapter

Use a graphing utility to find the indicated limit rounded to two decimal places.

limx鈫�-1x3+2x2+xx4+x3+2x+2

In Problems 53-56, use the properties of limits and the facts that

limx鈫�0sinxx=1limx鈫�0cosx-1x=1limx鈫�0sinx=0limx鈫�0cosx=1

limx鈫�03sinx+cosx-14x

In Problems 7鈥�16, use a table to find the indicated limit.

10.limx鈫�02-xx2+4.

In Problems 7鈥� 42, find each limit algebraically

limx鈫�15x4-3x2+6x-9

In Problems 7鈥� 42, find each limit algebraically.

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