## Thomas' Calculus 13th Edition

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