Find a formula for the error $E(x)$ in the tangent line approximation to the function $f(x) = \ln(x - 3)$ near $x = a = 4$.
$E(x) =$

Then fill in the following table of values for $E(x)/(x-a)$ near $x=a$

 $x =$ 4.1 4.01 4.001 $\frac{E(x)}{(x-a)} =$

Using your table, find a value of $k$ such that $E(x)/(x-a) \approx k(x-a)$.
$k =$

(Check that, approximately, $k=f''(a)/2$ and that $E(x) \approx (f''(a)/2)(x-a)^2$.