Let f(x) = tan(x). What is the formula for the conditioning number of f? Evaluate this formula for x =(π/4), 1.01, 1.26, 1.51 (in radians, working to 3 significant figures, the precision that is implicit in this data). Replace each of the expressions for x by its approximation ^x to 2 significant figures. Compute the relative error of the approximation ^x and the relative error of the approximation f(^x) to f(x).
Note: ^x is x-hat.