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: