Iterative methodsEdexcel International A Level Maths: Mind map

Exam questions on Iterative methods

1. The equation $x^3-4x-3=0$ has a root $\alpha$ with $2<\alpha<3$. The recurrence relation $x_{n+1}=\sqrt[3]{4x_n+3}$, with $x_0=2$, is used to find $\alpha$.
   Find $x_2$ and $x_3$, giving each to 4 decimal places.2 marks
2. The equation $f(x)=x^3+2x-7=0$ has a single real root $\alpha$.
   Use the iteration $x_{n+1}=\sqrt[3]{7-2x_n}$ with $x_0=1.5$ to find $x_2$, giving your answer to 3 decimal places.2 marks
3. The function $f(x)=\ln x+x-3$, for $x>0$, has a root $\alpha$.
   Show that $2<\alpha<2.5$.3 marks