$(1)$
\[
\left(h+\frac{H-h}{L}x\right)t
\]
$(2)$
$x$の位置における微小要素の伸びは,
\begin{align}
d\lambda&=\frac{Pdx}{A_{x}E}\\
&=\frac{P}{\left(h+\frac{H-h}{L}x\right)tE}dx
\end{align}
$(3)$
全体の伸びは積分すれば良い
\begin{align}
\lambda&=\int_0^Ld\lambda=\int_0^L\frac{P}{\left(h+\frac{H-h}{L}x\right)tE}dx\\
&=\frac{P}{tE}\int_0^L\frac{1}{{\left(h+\frac{H-h}{L}x\right)}}dx\\
&=\frac{P}{tE}\left[\log_{e}\left(h+\frac{H-h}{L}x\right)\frac{L}{H-h}\right]_0^L\\
&=\frac{P}{tE}\left\{\log_eH\frac{L}{H-h}-\log_eh\frac{L}{H-h}\right\}\\
&=\frac{PL}{tE}\frac{\log_e\frac{H}{h}}{H-h}\\
&=\frac{3000\times1}{\left(5\times10^{-3}\right)\times206\times10^9}\times\frac{\log_e\frac{30\times10^{-3}}{20\times10^{-3}}}{\left(30\times10^{-3}\right)-\left(20\times10^{-3}\right)}\\
&=1.18\times10^{-4}\ \textrm{m}
\end{align}
\end{enumerate}