(4) (a) Find the average value of $\cos t$ on the intervals $[0, \pi]$, $[0, \pi/2]$, $[0, \pi/4]$, $[0, 0.01]$. (b) Determine the general formula for $\bar{f}_{[0, x]}$, the average of $\cos t$ over the interval $[0, x]$. (c) Calculate $\lim_{x \to 0} \bar{f}_{[0, x]}$