$1)$ RC Transient Analysis: The switch begins in position $1$ and remained there for a long time. At $\backslash ($ t$=0\backslash ),$ the switched is moved to position $2.($a$)$ Find the equation for the voltage, $\backslash (\backslash$boldsymbol$\{$v$\}\backslash ),$ across the capacitor for $\backslash ($ t $\backslash$geq $0\backslash )$ and $($b$)$ sketch the capacitor voltage, $\backslash (\backslash$boldsymbol$\{$v$\}\backslash ),$ for $\backslash ($ t $\backslash$geq $0\backslash )($c$)$ at what time is the capacitor voltage, $\backslash (\backslash$boldsymbol$\{$v$\}\backslash ),$ approximately equal to zero $(\backslash (\backslash$boldsymbol$\{$v$\}=0\backslash )).$