   Chapter 2.6, Problem 11E

Chapter
Section
Textbook Problem

Guess the value of the limit lim x → ∞ x 2 2 x by evaluating the function f(x) = x2/2x for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 50, and 100. Then use a graph of f to support your guess.

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.

Explanation

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

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