## Thomas' Calculus 13th Edition

$\lt 1.87 \times 10^{-4}$
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 $\lt \dfrac{3^{0.1} \cdot (01)^{3} }{3!} \lt 1.87 \times 10^{-4}$