The function $g(x) = 2^x$ is graphed below, along with the tangent line to the graph at $x=0$.

Use the definition of the derivative, with $h=0.01$, to estimate the value of $g'(0)$.
$g'(0) \approx$

Use the definition of the derivative, with $h=0.001$, to estimate the value of $g'(0)$.
$g'(0) \approx$

Which of the following constants appears to be closest to $g'(0)$?
A. $\ln 2$
B. $2$
C. $\frac{1}{2}$
D. $0$
E. $1$
F. $\sqrt{e}$
G. None of these