# The value of lim x → ∞ x 2 2 x for the function f ( x ) = x 2 2 x for the values x = 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 20 , 50 and 100 .

### Single Variable Calculus: Concepts...

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

### 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 limx→∞x22x for the function f(x)=x22x for the valuesx=0,1,2,3,4,5,6,7,8,9,10,20,50 and 100.

Expert Solution

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 3.814697×10−4 50 2500 1.125899×1015 2.220446×10−12 100 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.

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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