**The question:**
Suppose that

i) Show that f is increasing on the interval [0, 1/2].

ii) Find the upper Riemann sum for f with respect to the partition

{

} of [0, 1/2]

iii) Hence evaluate limit n -> infinity (

)

**My attempt:**
i) I took the derivative of f, and found the stationary points by equating it to 0. I noticed that the only stationary point was at 0 itself, thus the graph may only change gradient at this point. I substituted for 1/2 and found that the gradient was positive, so the interval [0, 1/2] is increasing.

ii) I worked out the width of each partition is

, and the height of a given partition 'k' is

. My sum then looked something like this: