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Chapter 1: Q. 25 (page 107)

Use algebra to find the largest possible value of 未 or smallest possible value of N that makes each implication is true. Then verify and support your answers with labeled graphs.

If x鈭�1,1+未, then x-1-0<0.5

Short Answer

Expert verified

The required value of N is 未=0.25.

The required graph is given below,

Step by step solution

01

Step 1. Given information.

Consider the given question,

Ifx鈭�1,1+未, thenx-1-0<0.5.

02

Step 2. Find the value of δ.

Write the interval notation x鈭�1,1+未in inequality first:

1<x<1+未

Subtract 1from every side,

1-1<x-1<1+未-10<x-1<未

From x-1-0<0.5, we can write,

x-1-0<0.5x-1<0.5x-1<0.52x-1<0.25

As localid="1648277998405" 0<x-1<未, then,

未=0.25

03

Step 3. Sketching the function to illustrate the choice of δ.

Sketching the function, we get,

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