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Chapter 1: Q. 15 (page 107)

Determine whether each implication that follows is true or

false. Use graphs to justify any implications that are true and

counterexamples for any implications that are false.

If 0<|x-0|<0.75,then x2-0<0.5.

Short Answer

Expert verified

The implication is false.

Step by step solution

01

  Step 1. Given information. 

The given statement is the following.

If0<|x-0|<0.75thenx2-0<0.5.

02

Step 2. Justification.

Substitute x=-0.72in first inequality.

0<|x-0|<0.750<?|-0.72-0|<?0.750<0.72<0.75

Substitute x=-0.72in second inequality.

role="math" x2-0<0.5(-0.72)2-0<?0.50.5184鈮�0.5

The first inequality is satisfied at x=-0.72but the second inequality is not satisfied.

So the implication is false.

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