Given the function $f(x) = x^2 + 3$:  

1. Calculate the average rate of change from $x = 3$ to $x = 3.1$.

   Step (a):

   $\frac{f(3.1)-f(3)}{3.1-3}$

2. Determine the instantaneous rate of change at $x = 3$.

   Step (b):

   $\lim\limits_{h \to 0} \frac{f(3+h)-f(3)}{(3+h)-3}$