Which of the following have no real solutions?
(i) \(2x<2^x<x^2\quad\) (ii) \(x^2<2x<2^x\quad\) (iii) \(2^x<x^2<2x\quad\)
(iv) \(x^2<2^x<2x\quad\) (v) \(2^x<2x<x^2\quad\) (vi) \(2x<x^2<2^x\)
A (i) and (iii),\(\quad\) B (i) and (iv),\(\quad\) C (ii) and (iv),\(\quad\) D (ii) and (v),\(\quad\) E (iii) and (v)
Could we sketch the graphs of \(y=2x\), \(y=2^x\) and \(y = x^2\)?
Are there some values of \(x\) for which you know the order?
