## University Calculus: Early Transcendentals (3rd Edition)

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