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Chapter 14: Q. 7 (page 905)

find the limit limx鈫�1x-1x3-1

Short Answer

Expert verified

limx鈫�1x-1x3-1=13

Step by step solution

01

Step 1. Given information

limx鈫�1x-1x3-1

02

Step 2. Domain of the function

We can find limit of rational function by limx鈫�cf(x)=f(c) if c is in the domain of f(x) .So to find the domain of f(x)= x-1x3-1we have to put denominator =0

x3-1=0x=1

So the domain of f(x) is all real number except 1.

03

Step 3. limit of the function 

As c=1 in our limit so we have to simplify the f(x).

limx鈫�1x-1x3-1=limx鈫�1x-1(x-1)x2+x+1=limx鈫�11x2+x+1=1(1)2+(1)+1=13

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Most popular questions from this chapter

Iflimx鈫�cf(x)=f(c),thenfis______at__.

In Problems 45-60, determine whether fis continuous at c.

f(x)=x3-3x2+2x-6,c=2

True or False Some rational functions have holes in their graph.

In Problems 13鈥�32, use the accompanying graph of y = f(x).

Findlimx鈫�2-f(x).

In Problems 43-52, find the limit as xapproaches cof the average rate of change of each function from cto x.

c=1;f(x)=1x
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