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If y=(x)^{3x} for x>2 which of the following is true?

Option: 1

y<(3x)!


Option: 2

y<x!


Option: 3

(3x)!<(1.5x)^{3x}


Option: 4

Both A and C


Answers (1)

best_answer

 

 

Important Result (Comparison) -

\left ( \frac{n}{3} \right )^n<n!<\left (\frac{n}{2} \right )^n,\;\text{this result valid for }n>6

-

 

 

Let n=3x

hence, x=\frac{n}{3} \text{ hence, }n>6

now, y=\left ( \frac{n}{3} \right )^n

hence,

\\\left ( \frac{n}{3} \right )^n<n!<\left ( \frac{n}{2} \right )^n \\\\ \text{or,} \\\\ (x)^{3x}<\left ( 3x \right )!<(1.5x)^{3x}

option D is correct

Posted by

avinash.dongre

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