Chapter 10: Infinite Sequences and Series - Section 10.9 - Convergence of Taylor Series - Exercises 10.9 - Page 625: 42

$$\lt 1.67 \times 10^{-4}$$

Write the Taylor series for $ e^x=1+x +\dfrac{x^2}{2}+\dfrac{ x^3}{6}-....$ We need to apply the Remainder Estimation Theorem to calculate the error. $|R_2(x)| =|\dfrac{e^cx^3}{3!}| \\ \implies |R_2(x)| = |\dfrac{e^cx^3}{3!}| \times \dfrac{(0.1)^{3} }{3!}$ and $ \space Error \lt 1.67 \times 10^{-4}$