BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.5, Problem 11E
To determine

To evaluate: The value of limxx22x for the function f(x)=x22x for the values

x=0,1,2,3,4,5,6,7,8,9,10,20,50 and 100.

Expert Solution

Answer to Problem 11E

The value of limxx22x by evaluating the function f(x)=x22x for

x=0,1,2,3,4,5,6,7,8,9,10,20,50 and 100 is 0.

Explanation of Solution

Calculation:

Consider the function f(x)=x22x

The table value of the limit function f(x).

x x2 2x f(x)
0 0 1 0
1 1 2 0.5
2 4 4 1
3 9 8 1.125
4 16 16 1
5 25 32 0.78125
6 36 64 0.5625
7 49 128 0.3828125
8 64 256 0.25
9 81 512 0.15820313
10 100 1024 0.09765625
20 400 1048576 3.814697×104
50 2500 1.125899×1015 2.220446×1012
100 10000 1.267650×1030 0

From the table, it is concluded that limxx22x=0.

Graph:

Use the online graphing calculator to plot the graph of the function f(x)=x22x as shown in Figure1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.5, Problem 11E

From Figure1, it is observed that the curve approaches 0 as x approaches to infinity.

From the above graph, it is concluded that limxx22x=0.

Therefore, the graph supports the conclusion from the table values of f.

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