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Chapter 1: Q. 5 (page 97)

Find punctured intervals on which the function fx=1x2-xis defined, centered around

ax=1.5bx=0.25cx=1

Short Answer

Expert verified

Part (a). The punctured intervals is1,1.5鈭�1.5,2.

Part (b). The punctured intervals is0,0.25鈭�0.25,0.5.

Part (c). The punctured intervals is0,1鈭�1,2.

Step by step solution

01

Step 1. Given information. 

The given function isfx=1x2-x.

02

Part (a) Step 1. Calculation.

For x=1.5

The punctured intervalrole="math" localid="1649057100867" c-未,c鈭�c,c+未 is given by:
1.5-0.5,1.5鈭�1.5,1.5+0.5=1,1.5鈭�1.5,2.

03

Part (b) Step 1. Calculation.

For x=0.25

The punctured interval c-未,c鈭�c,c+未is given by:

0.25-0.25,0.25鈭�0.25,0.25+0.25=0,0.25鈭�0.25,0.5

04

Part (c) Step 1. Calculation.

For x=1

The punctured interval c-未,c鈭�c,c+未is given by:

1-1,1鈭�1,1+1=0,1鈭�1,2

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