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The functions $f$ and $g$ and their tangent lines at $(4,0)$ are shown in the figure below.

graph of f, a concave down function with positive slope, in blue; g, a concave up function with negative slope, in black, both of which pass through the point (4,0), and their tangent lines, graphed in red and green, respectively.

$f$ is shown in blue, $g$ in black, and the tangent line to $f$ is $y = 1 (x - 4)$ , and is graphed in red, and the tangent line to $g$ is $y = -0.5 (x - 4)$ , and is graphed in green.

Find the limit
$\displaystyle\lim_{x\to 4} \frac{f(x)}{g(x)} =$