Answer
$ 2.25$
Work Step by Step
From the given graph, we have
$\lim\limits_{x \to 2} \dfrac{f(x)}{g(x)} =\lim\limits_{x \to 2} \dfrac{f'(x)}{g'(x)} $
or, $\lim\limits_{x \to 2}\dfrac{1.8(x-2)}{\dfrac{4}{5}(x-2)} = \dfrac{0}{0}$
This shows is an indeterminate form.
Thus, on applying L'Hospital, we get
$=\lim\limits_{x \to 2} \dfrac{1.8(1)}{\dfrac{4}{5}(1)}$
$ = 2.25$
