$(1$ point$)$ Let $f(x)=ln(1+x).$

By considering the Taylor polynomial $T_2(x)$ of degree $2$ generated by $f(x)$ at the point $x=0,$ approximate $ln(1\mathrm{.}1)$ by $T_2(0\mathrm{.}1).ln(1\mathrm{.}1)$~~ $$

By Taylor's theorem, there exists cin$(0,0\mathrm{.}1)$ such that the error of the above approximation is $\frac{f^{\text{'}\text{'}\text{'}}(c)}{3!}(0\mathrm{.}1-0{)}^3.$

Hence, estimate the absolute error by giving an upper bound without $c.$

The absolute value $=|\frac{f^{\text{'}\text{'}\text{'}}(c)}{3!}(0\mathrm{.}1-0{)}^3|$

Remark: Instead of putting a large upper bound, You should give the upper bound as sharp as you can.