Answer
Four terms.
Work Step by Step
Consider $f(x)=e^x $
This gives: $f^n(x)=e^x$
Check the Taylor inequality at $x=0.1$
For this, we have $|R_n(x)|\leq \dfrac{M}{(n+1)!}|x-a|^{n+1}$
$\implies |R_2(x)|\leq \dfrac{e^{0.1}}{(2+1)!}|0.1-0|^{2+1}\approx 0.0002$
and $|R_3(x)|\leq \dfrac{e^{0.1}}{(3+1)!}|0.1-0|^{3+1}\approx 0.000005$
Here, it has been seen that $|R_3(x)| \lt 0.00001$ , so we need four terms.
