Statements (13) $\lim _ { x \rightarrow 0 } e ^ { \frac { 1 } { x } } = + \infty$. (14) The following inequality is true. $$\lim _ { x \rightarrow \infty } \frac { \ln x } { x ^ { 100 } } < \lim _ { x \rightarrow \infty } \frac { \ln x } { x ^ { \frac { 1 } { 100 } } }$$ (15) For any positive integer $n$, $$\int _ { - n } ^ { n } x ^ { 2023 } \cos ( n x ) \, dx < \frac { n } { 2023 }$$ (16) There is no polynomial $p ( x )$ for which there is a single line that is tangent to the graph of $p ( x )$ at exactly 100 points.
\textbf{Statements}
(13) $\lim _ { x \rightarrow 0 } e ^ { \frac { 1 } { x } } = + \infty$.\\
(14) The following inequality is true.
$$\lim _ { x \rightarrow \infty } \frac { \ln x } { x ^ { 100 } } < \lim _ { x \rightarrow \infty } \frac { \ln x } { x ^ { \frac { 1 } { 100 } } }$$
(15) For any positive integer $n$,
$$\int _ { - n } ^ { n } x ^ { 2023 } \cos ( n x ) \, dx < \frac { n } { 2023 }$$
(16) There is no polynomial $p ( x )$ for which there is a single line that is tangent to the graph of $p ( x )$ at exactly 100 points.