Find \(x\) in terms of \(t\) given that
\(4 \frac{\mathrm{~d}^{2} x}{\mathrm{~d} t^{2}}+4 \frac{\mathrm{~d} x}{\mathrm{~d} t}+x=6 \mathrm{e}^{-2 t}\)
and that, when \(t=0, x=\frac{5}{3}\) and \(\frac{\mathrm{d} x}{\mathrm{~d} t}=\frac{7}{6}\).

State \(\lim _{t \rightarrow \infty} x\).
[Questions 10 and 11 are printed on the next page.]