1. How many natural numbers $x$ satisfy the inequality $2014<\sqrt{x}<2015$?
$$
\begin{aligned}
& 2014<\sqrt{x}<2015 /^{2} \quad 1 \text { POINT } \\
& 2014^{2}<x<2015^{2} \quad 1 \text { POINT } \\
& 2015^{2}-2014^{2}=(2015-2014)(2015+2014)=4029 \quad 2 \text { POINTS } \\
& 2015^{2}-2014^{2}-1=4029-1=4028 . \quad 2 \text { POINTS }
\end{aligned}
$$