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Chapter 1: Q. 14 (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-2|<0.2,then x2-4<1.

Short Answer

Expert verified

The implication is true.

Step by step solution

01

  Step 1. Given information. 

The given statement is the following.

If 0<|x-2|<0.2,then x2-4<1.

02

Step 2. Justification.

Substitute x=1.9in first inequality.

0<|x-2|<0.20<?|1.9-2|<?0.20<?|0.1|<?0.20<0.1<0.2

Substitute x=1.9in second inequality.

role="math" x2-4<11.92-4<?1-0.39<?10.39<1

both inequalities are satisfied at role="math" localid="1648493836403" x=1.9.

so the implication is true.

03

Step 3. Graph of inequalities.

Plot the graph of both inequalities.The graph

Inequality0<|x-2|<0.2is within inequality x2-4<1.

so the implication is true.

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