With $\displaystyle{ f(x) = x^2 + 9 x + 1 \quad\text{ and }\quad a = 3 }$ and the given values of $h$, approximate the limit of the difference quotient: $$\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}.$$

1. When $h = 0.1$, $\displaystyle{ \frac{f(a+h) - f(a)}{h} }$ =
2. When $h = -0.1$, $\displaystyle{ \frac{f(a+h) - f(a)}{h} }$ =
3. When $h = 0.01$, $\displaystyle{ \frac{f(a+h) - f(a)}{h} }$ =
4. When $h = -0.01$, $\displaystyle{ \frac{f(a+h) - f(a)}{h} }$ =
5. Thus $\displaystyle{ \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} \approx }$