$(1$ point$)$ Let $f(x)=\sqrt[\phantom{2}]{x}.$

By considering the Taylor polynomial $T_2(x)$ of degree $2$ generated by $f(x)$ at the point $x=100,$ approximate $\sqrt[\phantom{2}]{105}$ by $T_2(105).$

$\sqrt[\phantom{2}]{105}$~~

$$

By Taylor's theorem, there exists cin$(100,105)$ such that the error of the above approximation is $\frac{f^{\text{'}\text{'}\text{'}}(c)}{3!}(105-100{)}^3.$

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

The absolute value $=|\frac{f^{\text{'}\text{'}\text{'}}(c)}{3!}(105-100{)}^3|$

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