Assume that $f:[0,1] \rightarrow \mathbb{R}$ is continuous on $[0,1]$ and differentiable on $(0,1)$ such that $f(x+h)=f(x)+h f^{\prime}(x+\theta h)$ for some $0<\theta<1$. If $f(x)=x^{2}(1+x)$, and $\theta$ is expressed in terms of $x$ and $h$, then the value of
\[
\lim _{h \rightarrow 0} \theta(x, h)
\]
is
- $\frac{1}{3}$
- $\frac{1}{2}$
- $\frac{1}{4}$
- $\frac{4}{5}$
