Find an expression for \(\frac { \mathrm { dy } } { \mathrm { dx } }\).
Show that the \(x\)-coordinate of \(M\) satisfies the equation \(x = \frac { x + 3 } { \ln ( 2 x + 1 ) } - 0.5\).
Show by calculation that the \(x\)-coordinate of \(M\) lies between 2.5 and 3.0 .
Use an iterative formula based on the equation in part (b) to find the \(x\)-coordinate of \(M\) correct to 4 significant figures. Give the result of each iteration to 6 significant figures.