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Chapter 1: Q. 18 (page 87)

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

(a) Show that f(x) is not defined at x = 2. How is this reflected in your calculator graph?

(b) Use the graph to argue that even though f(2) is undefined, we have limx鈫�2鈥�f(x)=13.

Short Answer

Expert verified

Part (a)

Part (b)13

Step by step solution

01

Part (a) Step 1. Given information.  

We have been given a function f(x)=x鈭�2x2鈭�x鈭�2.

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

Show that f(x) is not defined at x = 2. How this is reflected in the calculator graph.

02

Part (a) Step 2. Sketch the graph. 

Function is :

f(x)=x鈭�2x2鈭�x鈭�2

The graph of the function is :

From the graph, we see that at x=2, there is no any particular value of the function,
Put x=2 in the function :

f(2)=2鈭�222鈭�2鈭�2=04鈭�4=00

= undefined

03

Part (b) Step 1. Solving the limit expression 

Solving the limit expression,

We get:

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

=limx鈫�2鈥�1x+1=12+1=13

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