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Chapter 1: Q. 19 (page 87)

Use a calculator or other graphing utility to graph the function g(x)=x2鈭�2x+1x鈭�1.

(a) Show that g(x) is not defined at x = 1. How is this reflected in your calculator graph?

(b) Use the graph to argue that even though g(1) is undefined, we have limx鈫�1鈥�g(x)=0.

Short Answer

Expert verified

Part (a).

Part (b). 0

Step by step solution

01

Part (a) Step 1. Given information.   

We have been given a function g(x)=x2鈭�2x+1x鈭�1.

We have to use a calculator or other graphing utility to graph this function.

Show that g(x) is not defined at x = 1. How this is reflected in the calculator graph.

02

Part (a) Step 2. Sketch the graph. 

Function is :

g(x)=x2鈭�2x+1x鈭�1

The graph of the function is :

Putting x=1 in the function, we get:

g(1)=12鈭�2(1)+11鈭�1=1鈭�2+10=00

= Undefined

It is not immediately clear that g(x) IS not defined at x=1

03

Part (b) Step 1. Solving the limit expression.

Solving the limit expression,

limx鈫�1鈥�g(x)=limx鈫�1鈥�x2鈭�2x+1x鈭�1=limx鈫�1鈥�(x鈭�1)2x鈭�1=limx鈫�1鈥�(x鈭�1)=1鈭�1=0

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