Given $f(x,y,z)=ln(1xy2z)$ at the point $P(0,0,0)$

$($a$)$ Find the linear approximation to the function $f$ at the given point.

$($b$)$ Use part $($a$)$ to estimate $ln(1\mathrm{.}1)=f(0\mathrm{.}1,-0\mathrm{.}2,0\mathrm{.}1).$