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

Error $\leq 7.03 \times 10^{-4}$
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 $|f^{5} | \leq M$. So, $|R_n(x)| \leq M \dfrac{|x-a|^{n+1}}{(n+1)!}$ and $|R_4(0.5)| \leq (e^{1/2}) \times \dfrac{|0.5-0|^{5}}{5!} \approx 7.03 \times 10^{-4}$ So, Error $\leq 7.03 \times 10^{-4}$