HW1 1 The Maclaurin series expansion of arctan(x) is shown below 00 arctan(x)= (-1) 1+2n -x1+2n...

 

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HW1 1 The Maclaurin series expansion of arctan(x) is shown below 00 arctan(x)= (-1)" 1+2n -x1+2n =x-- + =0 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 of the 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. # Terms 1 2 3 Result 0.75 e% a% NA Note: The e calculation in the first iteration cannot be done as at this point there is no previous approximation. Hence, it should be left blank or filled with N/A. The value of e, can still be calculated as the true value is known. HW1 1 The Maclaurin series expansion of arctan(x) is shown below 00 arctan(x)= (-1)" 1+2n -x1+2n =x-- + =0 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 of the 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. # Terms 1 2 3 Result 0.75 e% a% NA Note: The e calculation in the first iteration cannot be done as at this point there is no previous approximation. Hence, it should be left blank or filled with N/A. The value of e, can still be calculated as the true value is known.