Answer
Please see below.
Work Step by Step
Looking at the graphs, we find that as $x$ approaches $0$, the functions $f(x)=x$ (the red graph)and $g(x)= \sin ^2 x$ (the blue graph) approach $0$, but the function $g(x)=\sin ^2 x$ approaches $0$ much more rapidly than the function $f(x)=x$ does. So, the function $h(x)=\frac{g(x)}{f(x)}= \frac{ \sin^2 x }{x}$ (the green graph) must approach $0$ when $x$ approaches $0$, as confirmed by the graph. Thus, we can conclude that$$\lim_{x \to 0} h(x)=0.$$
