Suppose \( f: R \rightarrow R \) is a differentiable function and \( f(1)=4 \). If \( \lim _{x \....

Suppose \( f: R \rightarrow R \) is a differentiable function and
\( \mathrm{P} \)
\( f(1)=4 \). If \( \lim _{x \rightarrow 1} \frac{\int_{4}^{f(x)} 2 t d t}{(x-1)}=k f^{\prime}(1) \), then \( k= \)