Problem 9: We are going to use the equation tan(%) = 1 to compute. Equivalently we are going to find a root of Tan(1/4)-1 Let solvep4[x_] := Tan[x] - 1. solvep4[x_] := Tan[x] - 1 D[solvep4 [x], x] Sec (x2 solvep4[x] solvep4' [x] Cos x)2 (-1 + Tan(x) ) Our iterating expression is X- solvep4[x] solvep4' [x] x - Cos(x)? (-1 + Tan [x]) A: The problem with this expression is that it has a square and a product in it, and two computations of trigonometric functions. Use TrigReduce to get a simpler expression. You should get 1 (1+2x+ Cos[2x]- Sin[2x]). This expression is computationally much simpler. There is no squaring, and the only product is multiplication (or division) by 2. B: Define newtsolvep4[x_]:=body by letting the simpler expression we got in A: to be the body of newtsolvep4. C: What is the smallest n such that Nest[newtsolvep4,N[1,200),n] gives at least 100 digits of Hint:Recall that the n-th entry of NestList[f,q,m) is f(n-1)(a) and that the last entry is fim (q). As we did with V2 get the list approx by using NestList. Get the list errors by subtracting from approx and then Map the function mag10 to error. As above to avoid getting huge exact expressions start at N[1,400] D: Use these results to get it rounded to 100 digits. Hint: multiply by 4 and then take estpi to be N[4 est,100] where est is the result of using Nest with the appropriate number of iterations. E: Compare with N[7,100]. Do we get the same decimal number. Hint you can look at two decimal numbers and compare them digit by digit or more easily you can use the logical relation=