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Chapter 7: Problem 5

If \(0

Short Answer

Expert verified
The correct statement is \(\sqrt{x}<x<1\).

Step by step solution

01

Examine option 1

This option suggests that \(x<\sqrt{x}<1\). Remembering that the square root function is increasing in the interval \((0, 1)\), this means that a number will always be less than its square root. However, this is not true in the interval \((0, 1)\), where a number is greater than its square root. Hence, this option is incorrect.
02

Examine option 2

Option 2 suggests \(x<1<\sqrt{x}\). This suggests that for \(0<x<1\), the square root of \(x\) is greater than 1. This is not true because when \(0<x<1\), \(x\) is less than 1 and hence, its square root is also less than 1. Hence, this option is not correct.
03

Examine option 3

Looking at option 3, \(\sqrt{x}<x<1\), it can be seen that this is indeed true. In the range \(0<x<1\), \(x\) is indeed greater than its square root and less than 1. Hence, this is the correct response option.

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Most popular questions from this chapter

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