(i)[2]
Using suitable sketches, show that the equation $e^{-\frac{1}{2}x} = 4 - x^2$ has one positive root and one negative root.
(ii)[2]
Verify by calculation that the negative root lies between $-1$ and $-1.5$.
(iii)[3]
Apply the iterative formula $x_{n+1} = -\sqrt{4 - e^{-\frac{1}{2}x_n}}$ to find this root correct to 2 decimal places. Write the result of each iteration to 4 decimal places.