Answer
$$\frac{1}{2}$$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow 1} \frac{1-\sqrt{x}}{1-x}&=\lim _{x \rightarrow 1} \frac{1-\sqrt{x}}{(1-\sqrt{x})(1+\sqrt{x})}\\
&=\lim _{x \rightarrow 1} \frac{1}{1+\sqrt{x}}\\
&=\frac{1}{2}
\end{align*}