CoursHeroTranscribedText: In this problem you will use the Taylor series 1) n $271+] 11-1 _ ( ._ _... (h) 2 2n+1 :"E 3+5 7+ "=0 to approximate the value of 7r. a. Substituting the value a: = 1 in the Taylor series above gives 7r_1 1+1 1+ 4 3 5 7 or equivalently, 4 4 4 =4*+**+"' 3 5 7 How many terms of this series would you need to add up, to obtain the value of 7r with an error of less than 0.01? b. We know that if z = a + bi and w = c + dii are complex numbers, then arg(zw) = arg(z) + arg(w). Use this fact to derive the following identity: tan'1 ad+bc =tan_1 9 +tan'l (if . acbd a c c. Using the formula in b: and the Taylor series of tanWm) show that 1 1 1 _ 1 -1 7r * 4 (tan (i) + tan (_)): Z(_l)n 271+ 1 (2211+1 + 32n+1> "=0 Calculate the first partial sum of this series which approximates 7r with an error of less than 0.01, and the partial sum which immediately follows it. Based on the fact that 11' lies between these two partial sums, conclude that 3.14] g 17 3 3.146