Chapter 9 - Section 9.9 - Convergence of Taylor Series - Exercises - Page 542: 42

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

The Taylor series for $ e^x $ can be defined as: $ e^x=1+x +\dfrac{x^2}{2}+\dfrac{ x^3}{6}-....$ Consider the Remainder Estimation Theorem to find the error. So, $|R_2(x)| =|\dfrac{e^cx^3}{3!}| $ and $|R_2(x)| = |\dfrac{e^cx^3}{3!}| \cdot \dfrac{(0.1)^{3} }{3!}$ So, Error $ \lt 1.67 \times 10^{-4}$