Solution:
The function is given below as
[tex]f(x)=\sqrt{50-3x},x_0=5.7[/tex]Concept:
The iteration formula will be given below as
[tex]x_{n+1}=\sqrt{50-3x_n}[/tex]Step 1:
To figure out the first iteration, we will use the formula below
[tex]\begin{gathered} x_1=f(x_0) \\ f(x_0)=\sqrt{50-3(5.7)} \\ f(x_0)=\sqrt{50-17.1} \\ f(x_{0)})=\sqrt{32.9} \\ f(x_0)=5.736 \end{gathered}[/tex][tex]\begin{gathered} x_2=f(x_1) \\ f(x_1)=\sqrt{50-3x} \\ f(x_1)=\sqrt{50-3(5.736)} \\ f(x_1)=5.726 \end{gathered}[/tex][tex]\begin{gathered} x_3=f(x_2) \\ f(x_2)=\sqrt{50-3x} \\ f(x_2)=\sqrt{50-3(5.726)} \\ f(x_2)=5.729 \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow x_3=5.729[/tex]OPTION B is the right answer
