(Solved): The Maclaurin series expansion of arctan(x) is shown below arctan() = (1) 1 + ...

The Maclaurin series expansion of arctan(x) is shown below arctan(????????) = ? (?1)???????? 1 + 2???????? ????????1+2???????? ? ????????=0 = ???????? ? ????????3 3 + ????????5 5 ? ????????7 7 + ????????9 9 ? ? Starting from the simplest version ????????????????????????????????????????????????(????????) = ????????, add terms one at a time to estimate arctan(0.75). After each term is added, calculate the true and approximate relative errors. Use your calculator for finding the ‘true’ value. Retain 5 decimal places in your calculations. Present your results in a tabular form like the one in Example 4.1 in your book. The template is given below, partially filled. Fill in empty boxes and add rows if necessary. Continue your calculations until you achieve 2 significant figures accuracy

HW1_1 The Maclaurin series expansion of arctan(x) is shown below $$\arctan (x)=\underset{n=0}{\overset{?}{?}}\frac{(?1{)}^n}{1+2n}{x}^{1+2n}=x?\frac{x^3}{3}+\frac{x^5}{5}?\frac{x^7}{7}+\frac{x^9}{9}??$$ Starting from the simplest version $$\arctan (x)=x$$, add terms one at a time to estimate arctan(0.75). After each term is added, calculate the true and approximate relative errors. Use your calculator for finding the 'true' value. Retain 5 decimal places in your calculations. Present your results in a tabular form like the one in Example $$4.1$$ in your book. The template is given below, partially filled. Fill in empty boxes and add rows if necessary. Continue your calculations until you achieve 2 significant figures accuracy.