(Solved): Please show the steps Given \( e^{x}=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\ldots \) If three te ...

Please show the steps

Given \( e^{x}=1+x+\frac{x^{2}}{2 !}+\frac{x^{3}}{3 !}+\ldots \) If three terms of the series are used to find \( e^{0.45} \), answer the following questions. Enter your answer in decimal format. What is the true error? What is the percentage relative true error? Give your answer as a percentage (report as a percent value, e.g., write down \( 45.89 \) for \( 45.89 \%) \) \( \% \) Solution The following are the correct answers. True error: \( 0.01706 \) Percentage relative true error: \( 1.088 \% \)