pr3tyana
Answered

if 0 < x < 1 , which of the following lists the numbers in increasing order ??

A√x , x , x²
Bx² , x , √x
Cx² , √x , x

Verified Answer :

darth666

answer B

\(x = \frac{1}{4}\)    
\(\sqrt{ \frac{1}{4} }= \frac{1}{2}\) 
\((\frac{1}{4})^2 = \frac{1}{16}\)

\(\frac{1}{16}\ \textless \ \frac{1}{4}\ \textless \ \frac{1}{2}\)

Answer:

(b) x² , x , √x

Step-by-step explanation:

Since, when x is a real number,

Such that 0 < x < 1

Then with increasing the exponent of x the value of x decreases,

That is, x with highest exponent is lowest,

Since,

\(2 > 1 > \frac{1}{2}\)

Thus, by the above statement,

\(x^2 < x < x^\frac{1}{2}\)

Hence, the numbers in increasing order is,

x² , x , √x

Where, 0 < x < 1

Option (b) is correct.

Related Questions