Vavali
If x is positive, which of the following could be correct ordering of \(\frac{1}{x}\), \(2x\), and \(x^2\)?
I. \(x^2 < 2x < \frac{1}{x}\)
II. \(x^2 < \frac{1}{x} < 2x\)
III. \(2x < x^2 < \frac{1}{x}\)
(A) none
(B) I only
(C) III only
(D) I and II
(E) I, II and III
Here, Since we are asked a possible ordering, we should check each equation for certain value. If none of the iterations are true for the equality, we can say that the equality is wrong and if even one is correct we will say that the equality is correct.
Here selecting numbers to test the equality is the tricky part.
let's say that we have the numbers 2x,1/x and x^2 to compare. obviously the equality will change depending on the value of x. Observe each individual equality and make a decision. ( i assumed 1/2,0.9,1.5,3)