Chapter 10: Infinite Sequences and Series - Section 10.9 - Convergence of Taylor Series - Exercises 10.9 - Page 625: 41

$\lt 1.87 \times 10^{-4}$

Write the Taylor series for $ e^x =1+x +\dfrac{x^2}{2}+\dfrac{ x^3}{6}-....$ Apply the Remainder Estimation Theorem to calculate the error. $|R_n(x)| \leq M \dfrac{|x-a|^{n+1}}{(n+1)!}$ $\implies |R_2(x)| \leq |\dfrac{e^ex^3}{3!}| $ and Error $ \lt \dfrac{3^{0.1} \cdot (01)^{3} }{3!} \lt 1.87 \times 10^{-4}$