By sketching a suitable pair of graphs, show that the equation
$$\ln x = 2 - x ^ { 2 }$$
has exactly one root.
Verify by calculation that the root lies between 1.0 and 1.4 .
Use the iterative formula
$$x _ { n + 1 } = \sqrt { } \left( 2 - \ln x _ { n } \right)$$
to determine the root correct to 2 decimal places, showing the result of each iteration.