Chapter 1: Q. 19 (page 87)

Use a calculator or other graphing utility to graph the function $g (x) = \frac{x^{2} - 2 x + 1}{x - 1}$ .
(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 $lim_{x \to 1} g (x) = 0$ .

Short Answer

Expert verified

Part (a).

Part (b). 0

Step by step solution

Part (a) Step 1. Given information.

We have been given a function $g (x) = \frac{x^{2} - 2 x + 1}{x - 1}$ .

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.

Part (a) Step 2. Sketch the graph.

Function is :

$g (x) = \frac{x^{2} - 2 x + 1}{x - 1}$

The graph of the function is :

Putting x=1 in the function, we get:

$\begin{aligned} g (1) = \frac{1^{2} - 2 (1) + 1}{1 - 1} \\ = \frac{1 - 2 + 1}{0} \\ = \frac{0}{0} \end{aligned}$

= Undefined

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

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

Solving the limit expression,

$\begin{aligned} lim_{x \to 1} g (x) = lim_{x \to 1} \frac{x^{2} - 2 x + 1}{x - 1} \\ = lim_{x \to 1} \frac{(x - 1)^{2}}{x - 1} \\ = lim_{x \to 1} (x - 1) \\ = 1 - 1 \\ = 0 \end{aligned}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use a calculator or other graphing utility to graph the function $g (x) = \frac{x^{2} - 2 x + 1}{x - 1}$ .
(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 $lim_{x \to 1} g (x) = 0$ .

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Sketch the graph.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Discrete Mathematics

Probability and Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use a calculator or other graphing utility to graph the function g(x)=x2−2x+1x−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→1 g(x)=0.

Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Sketch the graph.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Discrete Mathematics

Probability and Statistics

Geometry

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use a calculator or other graphing utility to graph the function $g (x) = \frac{x^{2} - 2 x + 1}{x - 1}$ .
(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 $lim_{x \to 1} g (x) = 0$ .