Chapter 9.1, Problem 43E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 41-44, graph each function with a graphing calculator and use it to predict the limit. Check your work either by using the table feature of the calculator or by finding the limit algebraically. lim x → − 1 x 3 − x x 2 + 2 x + 1

To determine

To graph: The function f(x)=x3xx2+2x+1 using a graphing calculator, and predict the limit, limx1x3xx2+2x+1. Also, check the limit.

Explanation

Given Information:

The function is f(x)=x3âˆ’xx2+2x+1.

The limit is limxâ†’âˆ’1x3âˆ’xx2+2x+1.

Graph:

Consider the provided function,

f(x)=x3âˆ’xx2+2x+1

Use the ti-83 graphing calculator to plot the graph.

Step 1: Open the ti-83 graphing calculator.

Step 2: Press the [Y=] key and enter the function in Y1, Y1=X3âˆ’XX2+2X+1.

Step 3: Press the [WINDOW] key and adjust the values accordingly.

Window:

Xmin=âˆ’10,Xmax=10,Xsc1=2Ymin=âˆ’10,Ymax=10,Ysc1=2

Step 4: Press the [TRACE] key.

Consider the provided limit,

limxâ†’âˆ’1x3âˆ’xx2+2x+1

The limit from the left is represented by limxâ†’âˆ’1âˆ’f(x) and the limit from the right is represented by limxâ†’âˆ’1+f(x).

The limxâ†’cf(x) will exist at c=âˆ’1 when the limit from the left, that is, the values of f(c) but c<âˆ’1, is equal to the limit from the right, that is, the values of f(c) but c>âˆ’1

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