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Chapter 1: Q. 16 (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 00<|x+2|<0.1,then x2-4<0.4.

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+2|<0.1,thenx2-4<0.4.

02

Step 2. Justification.

Substitute x=-1.9in first inequality.

0<|x+2|<0.10<|-1.9+2|<0.10<0.1鈮�0.1

substitute x=-1.9in second inequality.

x2-4<0.41.92-4<?0.40.39<0.4

The second inequality was satisfied but the first inequality did not satisfied.

So the implication is false.

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Most popular questions from this chapter

For each limit statement , use algebra to find 未 > 0 in terms of 蔚> 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < 蔚.

limx鈫�-2(4-2x)=8

Calculate each of the limits:

limh鈫�0(2+h)2-22h.

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem does not necessarily hold.

Calculate each of the limits:

limh鈫�0(-1+h)3-(-1)3h.

Write each of the inequalities in interval notation:

0<|x+3|<0.05
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